group_theory.schur_zassenhaus | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

d57133e4

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

6b31d1ee

bump to nightly-2024-03-17-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

22f01ce4

Diff

@@ -245,21 +245,21 @@ private theorem step2 (K : Subgroup G) [K.Normal] (hK : K ≤ N) : K = ⊥ ∨ K
   · rw [← comap_top (QuotientGroup.mk' K)]
     intro hH'
     rw [comap_injective this hH', is_complement'_top_right, map_eq_bot_iff,
-      QuotientGroup.ker_mk'] at hH 
+      QuotientGroup.ker_mk'] at hH
     · exact h4.2 (le_antisymm hK hH)
 
 /-- Do not use this lemma: It is made obsolete by `exists_right_complement'_of_coprime` -/
 private theorem step3 (K : Subgroup N) [(K.map N.Subtype).Normal] : K = ⊥ ∨ K = ⊤ :=
   by
   have key := step2 h1 h2 h3 (K.map N.subtype) K.map_subtype_le
-  rw [← map_bot N.subtype] at key 
+  rw [← map_bot N.subtype] at key
   conv at key =>
     congr
     skip
     rhs
     rw [← N.subtype_range, N.subtype.range_eq_map]
   have inj := map_injective N.subtype_injective
-  rwa [inj.eq_iff, inj.eq_iff] at key 
+  rwa [inj.eq_iff, inj.eq_iff] at key
 
 /-- Do not use this lemma: It is made obsolete by `exists_right_complement'_of_coprime` -/
 private theorem step4 : (Fintype.card N).minFac.Prime :=
@@ -306,7 +306,7 @@ private theorem exists_right_complement'_of_coprime_aux' [Fintype G] (hG : Finty
   rintro n ih G _ _ rfl N _ hN
   refine' not_forall_not.mp fun h3 => _
   haveI := schur_zassenhaus_induction.step7 hN (fun G' _ _ hG' => by apply ih _ hG'; rfl) h3
-  rw [← Nat.card_eq_fintype_card] at hN 
+  rw [← Nat.card_eq_fintype_card] at hN
   exact not_exists_of_forall_not h3 (exists_right_complement'_of_coprime_aux hN)
 
 #print Subgroup.exists_right_complement'_of_coprime_of_fintype /-
@@ -327,11 +327,11 @@ theorem exists_right_complement'_of_coprime {N : Subgroup G} [N.Normal]
     (hN : Nat.Coprime (Nat.card N) N.index) : ∃ H : Subgroup G, IsComplement' N H :=
   by
   by_cases hN1 : Nat.card N = 0
-  · rw [hN1, Nat.coprime_zero_left, index_eq_one] at hN 
+  · rw [hN1, Nat.coprime_zero_left, index_eq_one] at hN
     rw [hN]
     exact ⟨⊥, is_complement'_top_bot⟩
   by_cases hN2 : N.index = 0
-  · rw [hN2, Nat.coprime_zero_right] at hN 
+  · rw [hN2, Nat.coprime_zero_right] at hN
     haveI := (cardinal.to_nat_eq_one_iff_unique.mp hN).1
     rw [N.eq_bot_of_subsingleton]
     exact ⟨⊤, is_complement'_bot_top⟩
@@ -341,7 +341,7 @@ theorem exists_right_complement'_of_coprime {N : Subgroup G} [N.Normal]
   haveI :=
     (cardinal.lt_aleph_0_iff_fintype.mp
         (lt_of_not_ge (mt Cardinal.toNat_apply_of_aleph0_le hN3))).some
-  rw [Nat.card_eq_fintype_card] at hN 
+  rw [Nat.card_eq_fintype_card] at hN
   exact exists_right_complement'_of_coprime_of_fintype hN
 #align subgroup.exists_right_complement'_of_coprime Subgroup.exists_right_complement'_of_coprime
 -/

6b31d1ee

bump to nightly-2023-09-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2021 Thomas Browning. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Thomas Browning
 -/
-import Mathbin.GroupTheory.Sylow
-import Mathbin.GroupTheory.Transfer
+import GroupTheory.Sylow
+import GroupTheory.Transfer
 
 #align_import group_theory.schur_zassenhaus from "leanprover-community/mathlib"@"6b31d1eebd64eab86d5bd9936bfaada6ca8b5842"

6b31d1ee

bump to nightly-2023-09-20-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

e28e6964

Diff

@@ -109,7 +109,7 @@ theorem smul_diff' (h : H) :
 -/
 
 #print Subgroup.eq_one_of_smul_eq_one /-
-theorem eq_one_of_smul_eq_one (hH : Nat.coprime (Nat.card H) H.index) (α : H.QuotientDiff) (h : H) :
+theorem eq_one_of_smul_eq_one (hH : Nat.Coprime (Nat.card H) H.index) (α : H.QuotientDiff) (h : H) :
     h • α = α → h = 1 :=
   Quotient.inductionOn' α fun α hα =>
     (powCoprime hH).Injective <|
@@ -121,7 +121,7 @@ theorem eq_one_of_smul_eq_one (hH : Nat.coprime (Nat.card H) H.index) (α : H.Qu
 -/
 
 #print Subgroup.exists_smul_eq /-
-theorem exists_smul_eq (hH : Nat.coprime (Nat.card H) H.index) (α β : H.QuotientDiff) :
+theorem exists_smul_eq (hH : Nat.Coprime (Nat.card H) H.index) (α β : H.QuotientDiff) :
     ∃ h : H, h • α = β :=
   Quotient.inductionOn' α
     (Quotient.inductionOn' β fun β α =>
@@ -136,13 +136,13 @@ theorem exists_smul_eq (hH : Nat.coprime (Nat.card H) H.index) (α β : H.Quotie
 
 #print Subgroup.isComplement'_stabilizer_of_coprime /-
 theorem isComplement'_stabilizer_of_coprime {α : H.QuotientDiff}
-    (hH : Nat.coprime (Nat.card H) H.index) : IsComplement' H (stabilizer G α) :=
+    (hH : Nat.Coprime (Nat.card H) H.index) : IsComplement' H (stabilizer G α) :=
   isComplement'_stabilizer α (eq_one_of_smul_eq_one hH α) fun g => exists_smul_eq hH (g • α) α
 #align subgroup.is_complement'_stabilizer_of_coprime Subgroup.isComplement'_stabilizer_of_coprime
 -/
 
 /-- Do not use this lemma: It is made obsolete by `exists_right_complement'_of_coprime` -/
-private theorem exists_right_complement'_of_coprime_aux (hH : Nat.coprime (Nat.card H) H.index) :
+private theorem exists_right_complement'_of_coprime_aux (hH : Nat.Coprime (Nat.card H) H.index) :
     ∃ K : Subgroup G, IsComplement' H K :=
   instNonempty.elim fun α => ⟨stabilizer G α, isComplement'_stabilizer_of_coprime hH⟩
 
@@ -162,11 +162,11 @@ The proof is by contradiction. We assume that `G` is a minimal counterexample to
 
 
 variable {G : Type u} [Group G] [Fintype G] {N : Subgroup G} [Normal N]
-  (h1 : Nat.coprime (Fintype.card N) N.index)
+  (h1 : Nat.Coprime (Fintype.card N) N.index)
   (h2 :
     ∀ (G' : Type u) [Group G'] [Fintype G'],
       ∀ (hG'3 : Fintype.card G' < Fintype.card G) {N' : Subgroup G'} [N'.Normal]
-        (hN : Nat.coprime (Fintype.card N') N'.index), ∃ H' : Subgroup G', is_complement' N' H')
+        (hN : Nat.Coprime (Fintype.card N') N'.index), ∃ H' : Subgroup G', is_complement' N' H')
   (h3 : ∀ H : Subgroup G, ¬IsComplement' N H)
 
 /-! We will arrive at a contradiction via the following steps:
@@ -199,7 +199,7 @@ private theorem step1 (K : Subgroup G) (hK : K ⊔ N = ⊤) : K = ⊤ :=
     by
     rw [← K.index_mul_card]
     exact lt_mul_of_one_lt_left Fintype.card_pos (one_lt_index_of_ne_top h3)
-  have h6 : Nat.coprime (Fintype.card (N.comap K.subtype)) (N.comap K.subtype).index :=
+  have h6 : Nat.Coprime (Fintype.card (N.comap K.subtype)) (N.comap K.subtype).index :=
     by
     rw [h4]
     exact h1.coprime_dvd_left (card_comap_dvd_of_injective N K.subtype Subtype.coe_injective)
@@ -211,7 +211,7 @@ private theorem step1 (K : Subgroup G) (hK : K ⊔ N = ⊤) : K = ⊤ :=
       h4
   have h7 : Fintype.card N * Fintype.card (H.map K.subtype) = Fintype.card G := by
     rw [hH, ← N.index_mul_card, mul_comm]
-  have h8 : (Fintype.card N).coprime (Fintype.card (H.map K.subtype)) := by rwa [hH]
+  have h8 : (Fintype.card N).Coprime (Fintype.card (H.map K.subtype)) := by rwa [hH]
   exact ⟨H.map K.subtype, is_complement'_of_coprime h7 h8⟩
 
 /-- Do not use this lemma: It is made obsolete by `exists_right_complement'_of_coprime` -/
@@ -227,7 +227,7 @@ private theorem step2 (K : Subgroup G) [K.Normal] (hK : K ≤ N) : K = ⊥ ∨ K
       lt_mul_of_one_lt_right (Nat.pos_of_ne_zero index_ne_zero_of_finite)
         (K.one_lt_card_iff_ne_bot.mpr h4.1)
   have h6 :
-    Nat.coprime (Fintype.card (N.map (QuotientGroup.mk' K))) (N.map (QuotientGroup.mk' K)).index :=
+    Nat.Coprime (Fintype.card (N.map (QuotientGroup.mk' K))) (N.map (QuotientGroup.mk' K)).index :=
     by
     have index_map := N.index_map_eq this (by rwa [QuotientGroup.ker_mk'])
     have index_pos : 0 < N.index := Nat.pos_of_ne_zero index_ne_zero_of_finite
@@ -299,7 +299,7 @@ variable {n : ℕ} {G : Type u} [Group G]
 
 /-- Do not use this lemma: It is made obsolete by `exists_right_complement'_of_coprime` -/
 private theorem exists_right_complement'_of_coprime_aux' [Fintype G] (hG : Fintype.card G = n)
-    {N : Subgroup G} [N.Normal] (hN : Nat.coprime (Fintype.card N) N.index) :
+    {N : Subgroup G} [N.Normal] (hN : Nat.Coprime (Fintype.card N) N.index) :
     ∃ H : Subgroup G, IsComplement' N H := by
   revert G
   apply Nat.strong_induction_on n
@@ -314,7 +314,7 @@ private theorem exists_right_complement'_of_coprime_aux' [Fintype G] (hG : Finty
   If `H : subgroup G` is normal, and has order coprime to its index, then there exists a
   subgroup `K` which is a (right) complement of `H`. -/
 theorem exists_right_complement'_of_coprime_of_fintype [Fintype G] {N : Subgroup G} [N.Normal]
-    (hN : Nat.coprime (Fintype.card N) N.index) : ∃ H : Subgroup G, IsComplement' N H :=
+    (hN : Nat.Coprime (Fintype.card N) N.index) : ∃ H : Subgroup G, IsComplement' N H :=
   exists_right_complement'_of_coprime_aux' rfl hN
 #align subgroup.exists_right_complement'_of_coprime_of_fintype Subgroup.exists_right_complement'_of_coprime_of_fintype
 -/
@@ -324,7 +324,7 @@ theorem exists_right_complement'_of_coprime_of_fintype [Fintype G] {N : Subgroup
   If `H : subgroup G` is normal, and has order coprime to its index, then there exists a
   subgroup `K` which is a (right) complement of `H`. -/
 theorem exists_right_complement'_of_coprime {N : Subgroup G} [N.Normal]
-    (hN : Nat.coprime (Nat.card N) N.index) : ∃ H : Subgroup G, IsComplement' N H :=
+    (hN : Nat.Coprime (Nat.card N) N.index) : ∃ H : Subgroup G, IsComplement' N H :=
   by
   by_cases hN1 : Nat.card N = 0
   · rw [hN1, Nat.coprime_zero_left, index_eq_one] at hN 
@@ -351,7 +351,7 @@ theorem exists_right_complement'_of_coprime {N : Subgroup G} [N.Normal]
   If `H : subgroup G` is normal, and has order coprime to its index, then there exists a
   subgroup `K` which is a (left) complement of `H`. -/
 theorem exists_left_complement'_of_coprime_of_fintype [Fintype G] {N : Subgroup G} [N.Normal]
-    (hN : Nat.coprime (Fintype.card N) N.index) : ∃ H : Subgroup G, IsComplement' H N :=
+    (hN : Nat.Coprime (Fintype.card N) N.index) : ∃ H : Subgroup G, IsComplement' H N :=
   Exists.imp (fun _ => IsComplement'.symm) (exists_right_complement'_of_coprime_of_fintype hN)
 #align subgroup.exists_left_complement'_of_coprime_of_fintype Subgroup.exists_left_complement'_of_coprime_of_fintype
 -/
@@ -361,7 +361,7 @@ theorem exists_left_complement'_of_coprime_of_fintype [Fintype G] {N : Subgroup
   If `H : subgroup G` is normal, and has order coprime to its index, then there exists a
   subgroup `K` which is a (left) complement of `H`. -/
 theorem exists_left_complement'_of_coprime {N : Subgroup G} [N.Normal]
-    (hN : Nat.coprime (Nat.card N) N.index) : ∃ H : Subgroup G, IsComplement' H N :=
+    (hN : Nat.Coprime (Nat.card N) N.index) : ∃ H : Subgroup G, IsComplement' H N :=
   Exists.imp (fun _ => IsComplement'.symm) (exists_right_complement'_of_coprime hN)
 #align subgroup.exists_left_complement'_of_coprime Subgroup.exists_left_complement'_of_coprime
 -/

6b31d1ee

bump to nightly-2023-08-17-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

60285dcc

Diff

@@ -87,7 +87,7 @@ instance : MulAction G H.QuotientDiff
         (by
           rwa [smul_diff_smul', coe_mk, coe_one, mul_eq_one_iff_eq_inv, mul_right_eq_self, ←
             coe_one, ← Subtype.ext_iff])
-  mul_smul g₁ g₂ q :=
+  hMul_smul g₁ g₂ q :=
     Quotient.inductionOn' q fun T =>
       congr_arg Quotient.mk'' (by rw [mul_inv_rev] <;> exact mul_smul (op g₁⁻¹) (op g₂⁻¹) T)
   one_smul q :=

6b31d1ee

bump to nightly-2023-07-20-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Thomas Browning. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Thomas Browning
-
-! This file was ported from Lean 3 source module group_theory.schur_zassenhaus
-! leanprover-community/mathlib commit 6b31d1eebd64eab86d5bd9936bfaada6ca8b5842
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.GroupTheory.Sylow
 import Mathbin.GroupTheory.Transfer
 
+#align_import group_theory.schur_zassenhaus from "leanprover-community/mathlib"@"6b31d1eebd64eab86d5bd9936bfaada6ca8b5842"
+
 /-!
 # The Schur-Zassenhaus Theorem

6b31d1ee

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -54,6 +54,7 @@ def QuotientDiff :=
 instance : Inhabited H.QuotientDiff :=
   Quotient.inhabited _
 
+#print Subgroup.smul_diff_smul' /-
 theorem smul_diff_smul' [hH : Normal H] (g : Gᵐᵒᵖ) :
     diff (MonoidHom.id H) (g • α) (g • β) =
       ⟨g.unop⁻¹ * (diff (MonoidHom.id H) α β : H) * g.unop,
@@ -77,6 +78,7 @@ theorem smul_diff_smul' [hH : Normal H] (g : Gᵐᵒᵖ) :
   simp_rw [MonoidHom.id_apply, MonoidHom.coe_mk, coe_mk, smul_apply_eq_smul_apply_inv_smul,
     smul_eq_mul_unop, mul_inv_rev, mul_assoc]
 #align subgroup.smul_diff_smul' Subgroup.smul_diff_smul'
+-/
 
 variable {H} [Normal H]
 
@@ -95,6 +97,7 @@ instance : MulAction G H.QuotientDiff
     Quotient.inductionOn' q fun T =>
       congr_arg Quotient.mk'' (by rw [inv_one] <;> apply one_smul Gᵐᵒᵖ T)
 
+#print Subgroup.smul_diff' /-
 theorem smul_diff' (h : H) :
     diff (MonoidHom.id H) α (op (h : G) • β) = diff (MonoidHom.id H) α β * h ^ H.index :=
   by
@@ -106,7 +109,9 @@ theorem smul_diff' (h : H) :
     Equiv.apply_eq_iff_eq, inv_smul_eq_iff]
   exact self_eq_mul_right.mpr ((QuotientGroup.eq_one_iff _).mpr h.2)
 #align subgroup.smul_diff' Subgroup.smul_diff'
+-/
 
+#print Subgroup.eq_one_of_smul_eq_one /-
 theorem eq_one_of_smul_eq_one (hH : Nat.coprime (Nat.card H) H.index) (α : H.QuotientDiff) (h : H) :
     h • α = α → h = 1 :=
   Quotient.inductionOn' α fun α hα =>
@@ -116,7 +121,9 @@ theorem eq_one_of_smul_eq_one (hH : Nat.coprime (Nat.card H) H.index) (α : H.Qu
           rw [← diff_inv, smul_diff', diff_self, one_mul, inv_pow, inv_inv]
         _ = 1 ^ H.index := (Quotient.exact' hα).trans (one_pow H.index).symm
 #align subgroup.eq_one_of_smul_eq_one Subgroup.eq_one_of_smul_eq_one
+-/
 
+#print Subgroup.exists_smul_eq /-
 theorem exists_smul_eq (hH : Nat.coprime (Nat.card H) H.index) (α β : H.QuotientDiff) :
     ∃ h : H, h • α = β :=
   Quotient.inductionOn' α
@@ -128,11 +135,14 @@ theorem exists_smul_eq (hH : Nat.coprime (Nat.card H) H.index) (α β : H.Quotie
               ((smul_diff' β α ((powCoprime hH).symm (diff (MonoidHom.id H) β α))⁻¹).trans
                 (by rw [inv_pow, ← powCoprime_apply hH, Equiv.apply_symm_apply, mul_inv_self])))⟩)
 #align subgroup.exists_smul_eq Subgroup.exists_smul_eq
+-/
 
+#print Subgroup.isComplement'_stabilizer_of_coprime /-
 theorem isComplement'_stabilizer_of_coprime {α : H.QuotientDiff}
     (hH : Nat.coprime (Nat.card H) H.index) : IsComplement' H (stabilizer G α) :=
   isComplement'_stabilizer α (eq_one_of_smul_eq_one hH α) fun g => exists_smul_eq hH (g • α) α
 #align subgroup.is_complement'_stabilizer_of_coprime Subgroup.isComplement'_stabilizer_of_coprime
+-/
 
 /-- Do not use this lemma: It is made obsolete by `exists_right_complement'_of_coprime` -/
 private theorem exists_right_complement'_of_coprime_aux (hH : Nat.coprime (Nat.card H) H.index) :
@@ -162,8 +172,6 @@ variable {G : Type u} [Group G] [Fintype G] {N : Subgroup G} [Normal N]
         (hN : Nat.coprime (Fintype.card N') N'.index), ∃ H' : Subgroup G', is_complement' N' H')
   (h3 : ∀ H : Subgroup G, ¬IsComplement' N H)
 
-include h1 h2 h3
-
 /-! We will arrive at a contradiction via the following steps:
  * step 0: `N` (the normal Hall subgroup) is nontrivial.
  * step 1: If `K` is a subgroup of `G` with `K ⊔ N = ⊤`, then `K = ⊤`.
@@ -275,6 +283,7 @@ private theorem step6 : IsPGroup (Fintype.card N).minFac N :=
     normalizer_eq_top.mp (step1 h1 h2 h3 (P.1.map N.subtype).normalizer P.normalizer_sup_eq_top)
   exact (step3 h1 h2 h3 P.1).resolve_left (step5 h1 h2 h3)
 
+#print Subgroup.SchurZassenhausInduction.step7 /-
 /-- Do not use this lemma: It is made obsolete by `exists_right_complement'_of_coprime` -/
 theorem step7 : IsCommutative N :=
   by
@@ -285,6 +294,7 @@ theorem step7 : IsCommutative N :=
         eq_top_iff.mp ((step3 h1 h2 h3 N.center).resolve_left (step6 h1 h2 h3).bot_lt_center.ne')
           (mem_top h) g⟩⟩
 #align subgroup.schur_zassenhaus_induction.step7 Subgroup.SchurZassenhausInduction.step7
+-/
 
 end SchurZassenhausInduction
 
@@ -302,6 +312,7 @@ private theorem exists_right_complement'_of_coprime_aux' [Fintype G] (hG : Finty
   rw [← Nat.card_eq_fintype_card] at hN 
   exact not_exists_of_forall_not h3 (exists_right_complement'_of_coprime_aux hN)
 
+#print Subgroup.exists_right_complement'_of_coprime_of_fintype /-
 /-- **Schur-Zassenhaus** for normal subgroups:
   If `H : subgroup G` is normal, and has order coprime to its index, then there exists a
   subgroup `K` which is a (right) complement of `H`. -/
@@ -309,7 +320,9 @@ theorem exists_right_complement'_of_coprime_of_fintype [Fintype G] {N : Subgroup
     (hN : Nat.coprime (Fintype.card N) N.index) : ∃ H : Subgroup G, IsComplement' N H :=
   exists_right_complement'_of_coprime_aux' rfl hN
 #align subgroup.exists_right_complement'_of_coprime_of_fintype Subgroup.exists_right_complement'_of_coprime_of_fintype
+-/
 
+#print Subgroup.exists_right_complement'_of_coprime /-
 /-- **Schur-Zassenhaus** for normal subgroups:
   If `H : subgroup G` is normal, and has order coprime to its index, then there exists a
   subgroup `K` which is a (right) complement of `H`. -/
@@ -334,7 +347,9 @@ theorem exists_right_complement'_of_coprime {N : Subgroup G} [N.Normal]
   rw [Nat.card_eq_fintype_card] at hN 
   exact exists_right_complement'_of_coprime_of_fintype hN
 #align subgroup.exists_right_complement'_of_coprime Subgroup.exists_right_complement'_of_coprime
+-/
 
+#print Subgroup.exists_left_complement'_of_coprime_of_fintype /-
 /-- **Schur-Zassenhaus** for normal subgroups:
   If `H : subgroup G` is normal, and has order coprime to its index, then there exists a
   subgroup `K` which is a (left) complement of `H`. -/
@@ -342,7 +357,9 @@ theorem exists_left_complement'_of_coprime_of_fintype [Fintype G] {N : Subgroup
     (hN : Nat.coprime (Fintype.card N) N.index) : ∃ H : Subgroup G, IsComplement' H N :=
   Exists.imp (fun _ => IsComplement'.symm) (exists_right_complement'_of_coprime_of_fintype hN)
 #align subgroup.exists_left_complement'_of_coprime_of_fintype Subgroup.exists_left_complement'_of_coprime_of_fintype
+-/
 
+#print Subgroup.exists_left_complement'_of_coprime /-
 /-- **Schur-Zassenhaus** for normal subgroups:
   If `H : subgroup G` is normal, and has order coprime to its index, then there exists a
   subgroup `K` which is a (left) complement of `H`. -/
@@ -350,6 +367,7 @@ theorem exists_left_complement'_of_coprime {N : Subgroup G} [N.Normal]
     (hN : Nat.coprime (Nat.card N) N.index) : ∃ H : Subgroup G, IsComplement' H N :=
   Exists.imp (fun _ => IsComplement'.symm) (exists_right_complement'_of_coprime hN)
 #align subgroup.exists_left_complement'_of_coprime Subgroup.exists_left_complement'_of_coprime
+-/
 
 end Subgroup

6b31d1ee

bump to nightly-2023-06-10-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

e13a28eb

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Thomas Browning
 
 ! This file was ported from Lean 3 source module group_theory.schur_zassenhaus
-! leanprover-community/mathlib commit d57133e49cf06508700ef69030cd099917e0f0de
+! leanprover-community/mathlib commit 6b31d1eebd64eab86d5bd9936bfaada6ca8b5842
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.GroupTheory.Transfer
 /-!
 # The Schur-Zassenhaus Theorem
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we prove the Schur-Zassenhaus theorem.
 
 ## Main results

d57133e4

bump to nightly-2023-06-09-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

16afdc39

Diff

@@ -112,7 +112,6 @@ theorem eq_one_of_smul_eq_one (hH : Nat.coprime (Nat.card H) H.index) (α : H.Qu
         h ^ H.index = diff (MonoidHom.id H) (op ((h⁻¹ : H) : G) • α) α := by
           rw [← diff_inv, smul_diff', diff_self, one_mul, inv_pow, inv_inv]
         _ = 1 ^ H.index := (Quotient.exact' hα).trans (one_pow H.index).symm
-        
 #align subgroup.eq_one_of_smul_eq_one Subgroup.eq_one_of_smul_eq_one
 
 theorem exists_smul_eq (hH : Nat.coprime (Nat.card H) H.index) (α β : H.QuotientDiff) :

d57133e4

bump to nightly-2023-06-08-23

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

d3cfe2e3

Diff

@@ -129,7 +129,7 @@ theorem exists_smul_eq (hH : Nat.coprime (Nat.card H) H.index) (α β : H.Quotie
 
 theorem isComplement'_stabilizer_of_coprime {α : H.QuotientDiff}
     (hH : Nat.coprime (Nat.card H) H.index) : IsComplement' H (stabilizer G α) :=
-  IsComplement'_stabilizer α (eq_one_of_smul_eq_one hH α) fun g => exists_smul_eq hH (g • α) α
+  isComplement'_stabilizer α (eq_one_of_smul_eq_one hH α) fun g => exists_smul_eq hH (g • α) α
 #align subgroup.is_complement'_stabilizer_of_coprime Subgroup.isComplement'_stabilizer_of_coprime
 
 /-- Do not use this lemma: It is made obsolete by `exists_right_complement'_of_coprime` -/

d57133e4

bump to nightly-2023-06-07-23

mathlib commit https://github.com/leanprover-community/mathlib/commit/58a272265b5e05f258161260dd2c5d247213cbd3

c2a08841

Diff

@@ -38,6 +38,7 @@ open MulOpposite MulAction Subgroup.leftTransversals MemLeftTransversals
 variable {G : Type _} [Group G] (H : Subgroup G) [IsCommutative H] [FiniteIndex H]
   (α β : leftTransversals (H : Set G))
 
+#print Subgroup.QuotientDiff /-
 /-- The quotient of the transversals of an abelian normal `N` by the `diff` relation. -/
 def QuotientDiff :=
   Quotient
@@ -45,6 +46,7 @@ def QuotientDiff :=
       ⟨fun α => diff_self (MonoidHom.id H) α, fun α β h => by rw [← diff_inv, h, inv_one],
         fun α β γ h h' => by rw [← diff_mul_diff, h, h', one_mul]⟩)
 #align subgroup.quotient_diff Subgroup.QuotientDiff
+-/
 
 instance : Inhabited H.QuotientDiff :=
   Quotient.inhabited _

d57133e4

bump to nightly-2023-06-01-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

b9c87c70

Diff

@@ -236,21 +236,21 @@ private theorem step2 (K : Subgroup G) [K.Normal] (hK : K ≤ N) : K = ⊥ ∨ K
   · rw [← comap_top (QuotientGroup.mk' K)]
     intro hH'
     rw [comap_injective this hH', is_complement'_top_right, map_eq_bot_iff,
-      QuotientGroup.ker_mk'] at hH
+      QuotientGroup.ker_mk'] at hH 
     · exact h4.2 (le_antisymm hK hH)
 
 /-- Do not use this lemma: It is made obsolete by `exists_right_complement'_of_coprime` -/
 private theorem step3 (K : Subgroup N) [(K.map N.Subtype).Normal] : K = ⊥ ∨ K = ⊤ :=
   by
   have key := step2 h1 h2 h3 (K.map N.subtype) K.map_subtype_le
-  rw [← map_bot N.subtype] at key
+  rw [← map_bot N.subtype] at key 
   conv at key =>
     congr
     skip
     rhs
     rw [← N.subtype_range, N.subtype.range_eq_map]
   have inj := map_injective N.subtype_injective
-  rwa [inj.eq_iff, inj.eq_iff] at key
+  rwa [inj.eq_iff, inj.eq_iff] at key 
 
 /-- Do not use this lemma: It is made obsolete by `exists_right_complement'_of_coprime` -/
 private theorem step4 : (Fintype.card N).minFac.Prime :=
@@ -295,7 +295,7 @@ private theorem exists_right_complement'_of_coprime_aux' [Fintype G] (hG : Finty
   rintro n ih G _ _ rfl N _ hN
   refine' not_forall_not.mp fun h3 => _
   haveI := schur_zassenhaus_induction.step7 hN (fun G' _ _ hG' => by apply ih _ hG'; rfl) h3
-  rw [← Nat.card_eq_fintype_card] at hN
+  rw [← Nat.card_eq_fintype_card] at hN 
   exact not_exists_of_forall_not h3 (exists_right_complement'_of_coprime_aux hN)
 
 /-- **Schur-Zassenhaus** for normal subgroups:
@@ -313,11 +313,11 @@ theorem exists_right_complement'_of_coprime {N : Subgroup G} [N.Normal]
     (hN : Nat.coprime (Nat.card N) N.index) : ∃ H : Subgroup G, IsComplement' N H :=
   by
   by_cases hN1 : Nat.card N = 0
-  · rw [hN1, Nat.coprime_zero_left, index_eq_one] at hN
+  · rw [hN1, Nat.coprime_zero_left, index_eq_one] at hN 
     rw [hN]
     exact ⟨⊥, is_complement'_top_bot⟩
   by_cases hN2 : N.index = 0
-  · rw [hN2, Nat.coprime_zero_right] at hN
+  · rw [hN2, Nat.coprime_zero_right] at hN 
     haveI := (cardinal.to_nat_eq_one_iff_unique.mp hN).1
     rw [N.eq_bot_of_subsingleton]
     exact ⟨⊤, is_complement'_bot_top⟩
@@ -327,7 +327,7 @@ theorem exists_right_complement'_of_coprime {N : Subgroup G} [N.Normal]
   haveI :=
     (cardinal.lt_aleph_0_iff_fintype.mp
         (lt_of_not_ge (mt Cardinal.toNat_apply_of_aleph0_le hN3))).some
-  rw [Nat.card_eq_fintype_card] at hN
+  rw [Nat.card_eq_fintype_card] at hN 
   exact exists_right_complement'_of_coprime_of_fintype hN
 #align subgroup.exists_right_complement'_of_coprime Subgroup.exists_right_complement'_of_coprime

d57133e4

bump to nightly-2023-06-01-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

4d9eaa85

Diff

@@ -127,7 +127,7 @@ theorem exists_smul_eq (hH : Nat.coprime (Nat.card H) H.index) (α β : H.Quotie
 
 theorem isComplement'_stabilizer_of_coprime {α : H.QuotientDiff}
     (hH : Nat.coprime (Nat.card H) H.index) : IsComplement' H (stabilizer G α) :=
-  isComplement'_stabilizer α (eq_one_of_smul_eq_one hH α) fun g => exists_smul_eq hH (g • α) α
+  IsComplement'_stabilizer α (eq_one_of_smul_eq_one hH α) fun g => exists_smul_eq hH (g • α) α
 #align subgroup.is_complement'_stabilizer_of_coprime Subgroup.isComplement'_stabilizer_of_coprime
 
 /-- Do not use this lemma: It is made obsolete by `exists_right_complement'_of_coprime` -/

d57133e4

bump to nightly-2023-05-28-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

8d353152

Diff

@@ -27,7 +27,7 @@ In this file we prove the Schur-Zassenhaus theorem.
 -/
 
 
-open BigOperators
+open scoped BigOperators
 
 namespace Subgroup
 
@@ -137,7 +137,7 @@ private theorem exists_right_complement'_of_coprime_aux (hH : Nat.coprime (Nat.c
 
 end SchurZassenhausAbelian
 
-open Classical
+open scoped Classical
 
 universe u

d57133e4

bump to nightly-2023-05-28-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6797a637

Diff

@@ -294,12 +294,7 @@ private theorem exists_right_complement'_of_coprime_aux' [Fintype G] (hG : Finty
   apply Nat.strong_induction_on n
   rintro n ih G _ _ rfl N _ hN
   refine' not_forall_not.mp fun h3 => _
-  haveI :=
-    schur_zassenhaus_induction.step7 hN
-      (fun G' _ _ hG' => by
-        apply ih _ hG'
-        rfl)
-      h3
+  haveI := schur_zassenhaus_induction.step7 hN (fun G' _ _ hG' => by apply ih _ hG'; rfl) h3
   rw [← Nat.card_eq_fintype_card] at hN
   exact not_exists_of_forall_not h3 (exists_right_complement'_of_coprime_aux hN)

d57133e4

bump to nightly-2023-05-28-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6c6011cf

Diff

@@ -134,7 +134,6 @@ theorem isComplement'_stabilizer_of_coprime {α : H.QuotientDiff}
 private theorem exists_right_complement'_of_coprime_aux (hH : Nat.coprime (Nat.card H) H.index) :
     ∃ K : Subgroup G, IsComplement' H K :=
   instNonempty.elim fun α => ⟨stabilizer G α, isComplement'_stabilizer_of_coprime hH⟩
-#align subgroup.exists_right_complement'_of_coprime_aux subgroup.exists_right_complement'_of_coprime_aux
 
 end SchurZassenhausAbelian
 
@@ -178,7 +177,6 @@ include h1 h2 h3
 private theorem step0 : N ≠ ⊥ := by
   rintro rfl
   exact h3 ⊤ is_complement'_bot_top
-#align subgroup.schur_zassenhaus_induction.step0 subgroup.schur_zassenhaus_induction.step0
 
 /-- Do not use this lemma: It is made obsolete by `exists_right_complement'_of_coprime` -/
 private theorem step1 (K : Subgroup G) (hK : K ⊔ N = ⊤) : K = ⊤ :=
@@ -206,7 +204,6 @@ private theorem step1 (K : Subgroup G) (hK : K ⊔ N = ⊤) : K = ⊤ :=
     rw [hH, ← N.index_mul_card, mul_comm]
   have h8 : (Fintype.card N).coprime (Fintype.card (H.map K.subtype)) := by rwa [hH]
   exact ⟨H.map K.subtype, is_complement'_of_coprime h7 h8⟩
-#align subgroup.schur_zassenhaus_induction.step1 subgroup.schur_zassenhaus_induction.step1
 
 /-- Do not use this lemma: It is made obsolete by `exists_right_complement'_of_coprime` -/
 private theorem step2 (K : Subgroup G) [K.Normal] (hK : K ≤ N) : K = ⊥ ∨ K = N :=
@@ -241,7 +238,6 @@ private theorem step2 (K : Subgroup G) [K.Normal] (hK : K ≤ N) : K = ⊥ ∨ K
     rw [comap_injective this hH', is_complement'_top_right, map_eq_bot_iff,
       QuotientGroup.ker_mk'] at hH
     · exact h4.2 (le_antisymm hK hH)
-#align subgroup.schur_zassenhaus_induction.step2 subgroup.schur_zassenhaus_induction.step2
 
 /-- Do not use this lemma: It is made obsolete by `exists_right_complement'_of_coprime` -/
 private theorem step3 (K : Subgroup N) [(K.map N.Subtype).Normal] : K = ⊥ ∨ K = ⊤ :=
@@ -255,18 +251,15 @@ private theorem step3 (K : Subgroup N) [(K.map N.Subtype).Normal] : K = ⊥ ∨
     rw [← N.subtype_range, N.subtype.range_eq_map]
   have inj := map_injective N.subtype_injective
   rwa [inj.eq_iff, inj.eq_iff] at key
-#align subgroup.schur_zassenhaus_induction.step3 subgroup.schur_zassenhaus_induction.step3
 
 /-- Do not use this lemma: It is made obsolete by `exists_right_complement'_of_coprime` -/
 private theorem step4 : (Fintype.card N).minFac.Prime :=
   Nat.minFac_prime (N.one_lt_card_iff_ne_bot.mpr (step0 h1 h2 h3)).ne'
-#align subgroup.schur_zassenhaus_induction.step4 subgroup.schur_zassenhaus_induction.step4
 
 /-- Do not use this lemma: It is made obsolete by `exists_right_complement'_of_coprime` -/
 private theorem step5 {P : Sylow (Fintype.card N).minFac N} : P.1 ≠ ⊥ :=
   haveI : Fact (Fintype.card N).minFac.Prime := ⟨step4 h1 h2 h3⟩
   P.ne_bot_of_dvd_card (Fintype.card N).minFac_dvd
-#align subgroup.schur_zassenhaus_induction.step5 subgroup.schur_zassenhaus_induction.step5
 
 /-- Do not use this lemma: It is made obsolete by `exists_right_complement'_of_coprime` -/
 private theorem step6 : IsPGroup (Fintype.card N).minFac N :=
@@ -277,7 +270,6 @@ private theorem step6 : IsPGroup (Fintype.card N).minFac N :=
   haveI : (P.1.map N.subtype).Normal :=
     normalizer_eq_top.mp (step1 h1 h2 h3 (P.1.map N.subtype).normalizer P.normalizer_sup_eq_top)
   exact (step3 h1 h2 h3 P.1).resolve_left (step5 h1 h2 h3)
-#align subgroup.schur_zassenhaus_induction.step6 subgroup.schur_zassenhaus_induction.step6
 
 /-- Do not use this lemma: It is made obsolete by `exists_right_complement'_of_coprime` -/
 theorem step7 : IsCommutative N :=
@@ -310,7 +302,6 @@ private theorem exists_right_complement'_of_coprime_aux' [Fintype G] (hG : Finty
       h3
   rw [← Nat.card_eq_fintype_card] at hN
   exact not_exists_of_forall_not h3 (exists_right_complement'_of_coprime_aux hN)
-#align subgroup.exists_right_complement'_of_coprime_aux' subgroup.exists_right_complement'_of_coprime_aux'
 
 /-- **Schur-Zassenhaus** for normal subgroups:
   If `H : subgroup G` is normal, and has order coprime to its index, then there exists a

d57133e4

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

d57133e4

chore: avoid automatically generated instance names (#12270)

47e1ef4b

Diff

@@ -122,7 +122,8 @@ theorem isComplement'_stabilizer_of_coprime {α : H.QuotientDiff}
 /-- Do not use this lemma: It is made obsolete by `exists_right_complement'_of_coprime` -/
 private theorem exists_right_complement'_of_coprime_aux (hH : Nat.Coprime (Nat.card H) H.index) :
     ∃ K : Subgroup G, IsComplement' H K :=
-  instNonempty.elim fun α => ⟨stabilizer G α, isComplement'_stabilizer_of_coprime hH⟩
+  have ne : Nonempty (QuotientDiff H) := inferInstance
+  ne.elim fun α => ⟨stabilizer G α, isComplement'_stabilizer_of_coprime hH⟩
 
 end SchurZassenhausAbelian

d57133e4

chore: tidy various files (#11135)

1384de0d

Diff

@@ -15,10 +15,10 @@ In this file we prove the Schur-Zassenhaus theorem.
 
 ## Main results
 
-- `exists_right_complement'_of_coprime` : The **Schur-Zassenhaus** theorem:
+- `exists_right_complement'_of_coprime`: The **Schur-Zassenhaus** theorem:
   If `H : Subgroup G` is normal and has order coprime to its index,
   then there exists a subgroup `K` which is a (right) complement of `H`.
-- `exists_left_complement'_of_coprime` : The **Schur-Zassenhaus** theorem:
+- `exists_left_complement'_of_coprime`: The **Schur-Zassenhaus** theorem:
   If `H : Subgroup G` is normal and has order coprime to its index,
   then there exists a subgroup `K` which is a (left) complement of `H`.
 -/

d57133e4

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

converts "--porting note" into "-- Porting note";
converts "porting note" into "Porting note".

8be0b69c

Diff

@@ -44,7 +44,7 @@ def QuotientDiff :=
 #align subgroup.quotient_diff Subgroup.QuotientDiff
 
 instance : Inhabited H.QuotientDiff := by
-  dsimp [QuotientDiff] -- porting note: Added `dsimp`
+  dsimp [QuotientDiff] -- Porting note: Added `dsimp`
   infer_instance
 
 theorem smul_diff_smul' [hH : Normal H] (g : Gᵐᵒᵖ) :

d57133e4

chore: prepare Lean version bump with explicit simp (#10999)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

38bce757

Diff

@@ -60,7 +60,7 @@ theorem smul_diff_smul' [hH : Normal H] (g : Gᵐᵒᵖ) :
       map_mul' := fun h₁ h₂ => by
         simp only [Subtype.ext_iff, coe_mk, coe_mul, mul_assoc, mul_inv_cancel_left] }
   refine (Fintype.prod_equiv (MulAction.toPerm g).symm _ _ fun x ↦ ?_).trans (map_prod ϕ _ _).symm
-  simp only [smul_apply_eq_smul_apply_inv_smul, smul_eq_mul_unop, mul_inv_rev, mul_assoc,
+  simp only [ϕ, smul_apply_eq_smul_apply_inv_smul, smul_eq_mul_unop, mul_inv_rev, mul_assoc,
     MonoidHom.id_apply, toPerm_symm_apply, MonoidHom.coe_mk, OneHom.coe_mk]
 #align subgroup.smul_diff_smul' Subgroup.smul_diff_smul'

d57133e4

feat: Add lattice lemmas about Sub{group,monoid}.{op,unop} (#9860)

In fact I only need the closure lemma, but the others are easy enough.

This changes the opEquivs to be order isomorphisms rather than just Equivs.

f1802b11

Diff

@@ -86,8 +86,8 @@ theorem smul_diff' (h : H) :
   rw [diff, diff, index_eq_card, ← Finset.card_univ, ← Finset.prod_const, ← Finset.prod_mul_distrib]
   refine' Finset.prod_congr rfl fun q _ => _
   simp_rw [Subtype.ext_iff, MonoidHom.id_apply, coe_mul, mul_assoc, mul_right_inj]
-  rw [smul_apply_eq_smul_apply_inv_smul, smul_eq_mul_unop, unop_op, mul_left_inj, ← Subtype.ext_iff,
-    Equiv.apply_eq_iff_eq, inv_smul_eq_iff]
+  rw [smul_apply_eq_smul_apply_inv_smul, smul_eq_mul_unop, MulOpposite.unop_op, mul_left_inj,
+    ← Subtype.ext_iff, Equiv.apply_eq_iff_eq, inv_smul_eq_iff]
   exact self_eq_mul_right.mpr ((QuotientGroup.eq_one_iff _).mpr h.2)
 #align subgroup.smul_diff' Subgroup.smul_diff'

d57133e4

feat: Better lemmas for transferring finite sums along equivalences (#9237)

Lemmas around this were a mess, throth in terms of names, statement and location. This PR standardises everything to be in Algebra.BigOperators.Basic and changes the lemmas to take in InjOn and SurjOn assumptions where possible (and where impossible make sure the hypotheses are taken in the correct order) and moves the equality of functions hypothesis last.

Also add a few lemmas that help fix downstream uses by golfing.

From LeanAPAP and LeanCamCombi

82c60323

Diff

@@ -59,14 +59,9 @@ theorem smul_diff_smul' [hH : Normal H] (g : Gᵐᵒᵖ) :
       map_one' := by rw [Subtype.ext_iff, coe_mk, coe_one, mul_one, inv_mul_self]
       map_mul' := fun h₁ h₂ => by
         simp only [Subtype.ext_iff, coe_mk, coe_mul, mul_assoc, mul_inv_cancel_left] }
-  refine'
-    Eq.trans
-      (Finset.prod_bij' (fun q _ => g⁻¹ • q) (fun q _ => Finset.mem_univ _)
-        (fun q _ => Subtype.ext _) (fun q _ => g • q) (fun q _ => Finset.mem_univ _)
-        (fun q _ => smul_inv_smul g q) fun q _ => inv_smul_smul g q)
-      (map_prod ϕ _ _).symm
-  simp only [MonoidHom.id_apply, MonoidHom.coe_mk, OneHom.coe_mk,
-    smul_apply_eq_smul_apply_inv_smul, smul_eq_mul_unop, mul_inv_rev, mul_assoc]
+  refine (Fintype.prod_equiv (MulAction.toPerm g).symm _ _ fun x ↦ ?_).trans (map_prod ϕ _ _).symm
+  simp only [smul_apply_eq_smul_apply_inv_smul, smul_eq_mul_unop, mul_inv_rev, mul_assoc,
+    MonoidHom.id_apply, toPerm_symm_apply, MonoidHom.coe_mk, OneHom.coe_mk]
 #align subgroup.smul_diff_smul' Subgroup.smul_diff_smul'
 
 variable {H} [Normal H]

d57133e4

chore(*): use ∃ x ∈ s, _ instead of ∃ (x) (_ : x ∈ s), _ (#9215)

Follow-up #9184

ef974f86

Diff

@@ -146,10 +146,9 @@ The proof is by contradiction. We assume that `G` is a minimal counterexample to
 
 variable {G : Type u} [Group G] [Fintype G] {N : Subgroup G} [Normal N]
   (h1 : Nat.Coprime (Fintype.card N) N.index)
-  (h2 :
-    ∀ (G' : Type u) [Group G'] [Fintype G'],
-      ∀ (_ : Fintype.card G' < Fintype.card G) {N' : Subgroup G'} [N'.Normal]
-        (_ : Nat.Coprime (Fintype.card N') N'.index), ∃ H' : Subgroup G', IsComplement' N' H')
+  (h2 : ∀ (G' : Type u) [Group G'] [Fintype G'],
+    Fintype.card G' < Fintype.card G → ∀ {N' : Subgroup G'} [N'.Normal],
+      Nat.Coprime (Fintype.card N') N'.index → ∃ H' : Subgroup G', IsComplement' N' H')
   (h3 : ∀ H : Subgroup G, ¬IsComplement' N H)
 
 /-! We will arrive at a contradiction via the following steps:

d57133e4

chore: space after ← (#8178)

Co-authored-by: Moritz Firsching <firsching@google.com>

5fb9beab

Diff

@@ -88,10 +88,10 @@ noncomputable instance : MulAction G H.QuotientDiff where
 theorem smul_diff' (h : H) :
     diff (MonoidHom.id H) α (op (h : G) • β) = diff (MonoidHom.id H) α β * h ^ H.index := by
   letI := H.fintypeQuotientOfFiniteIndex
-  rw [diff, diff, index_eq_card, ←Finset.card_univ, ←Finset.prod_const, ←Finset.prod_mul_distrib]
+  rw [diff, diff, index_eq_card, ← Finset.card_univ, ← Finset.prod_const, ← Finset.prod_mul_distrib]
   refine' Finset.prod_congr rfl fun q _ => _
   simp_rw [Subtype.ext_iff, MonoidHom.id_apply, coe_mul, mul_assoc, mul_right_inj]
-  rw [smul_apply_eq_smul_apply_inv_smul, smul_eq_mul_unop, unop_op, mul_left_inj, ←Subtype.ext_iff,
+  rw [smul_apply_eq_smul_apply_inv_smul, smul_eq_mul_unop, unop_op, mul_left_inj, ← Subtype.ext_iff,
     Equiv.apply_eq_iff_eq, inv_smul_eq_iff]
   exact self_eq_mul_right.mpr ((QuotientGroup.eq_one_iff _).mpr h.2)
 #align subgroup.smul_diff' Subgroup.smul_diff'
@@ -183,9 +183,9 @@ private theorem step1 (K : Subgroup G) (hK : K ⊔ N = ⊤) : K = ⊤ := by
     exact h1.coprime_dvd_left (card_comap_dvd_of_injective N K.subtype Subtype.coe_injective)
   obtain ⟨H, hH⟩ := h2 K h5 h6
   replace hH : Fintype.card (H.map K.subtype) = N.index := by
-    rw [←relindex_bot_left_eq_card, ←relindex_comap, MonoidHom.comap_bot, Subgroup.ker_subtype,
-      relindex_bot_left, ←IsComplement'.index_eq_card (IsComplement'.symm hH), index_comap,
-      subtype_range, ←relindex_sup_right, hK, relindex_top_right]
+    rw [← relindex_bot_left_eq_card, ← relindex_comap, MonoidHom.comap_bot, Subgroup.ker_subtype,
+      relindex_bot_left, ← IsComplement'.index_eq_card (IsComplement'.symm hH), index_comap,
+      subtype_range, ← relindex_sup_right, hK, relindex_top_right]
   have h7 : Fintype.card N * Fintype.card (H.map K.subtype) = Fintype.card G := by
     rw [hH, ← N.index_mul_card, mul_comm]
   have h8 : (Fintype.card N).Coprime (Fintype.card (H.map K.subtype)) := by
@@ -304,7 +304,7 @@ theorem exists_right_complement'_of_coprime {N : Subgroup G} [N.Normal]
   haveI := (Cardinal.lt_aleph0_iff_fintype.mp
     (lt_of_not_ge (mt Cardinal.toNat_apply_of_aleph0_le hN3))).some
   apply exists_right_complement'_of_coprime_of_fintype
-  rwa [←Nat.card_eq_fintype_card]
+  rwa [← Nat.card_eq_fintype_card]
 #align subgroup.exists_right_complement'_of_coprime Subgroup.exists_right_complement'_of_coprime
 
 /-- **Schur-Zassenhaus** for normal subgroups:

d57133e4

refactor(Algebra): Define the center appropriately for non-associative algebras (#6996)

For a sensible theory, we require that the centre of an algebra is closed under multiplication. The definition currently in Mathlib works for associative algebras, but not non-associative algebras. This PR uses the definition from Cabrera García and Rodríguez Palacios, which works for any multiplication (addition) and which coincides with the current definition in the associative case.

I did consider whether the centralizer should also be re-defined in terms of operator commutation, but this still results in a centralizer which is not closed under multiplication in the non-associative case. I have therefore retained the current definition, but changed centralizer_eq_top_iff_subset and centralizer_univ to only work in the associative case.

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Christopher Hoskin <mans0954@users.noreply.github.com> Co-authored-by: Christopher Hoskin <christopher.hoskin@overleaf.com>

2fed2bb8

Diff

@@ -256,9 +256,8 @@ theorem step7 : IsCommutative N := by
   haveI := N.bot_or_nontrivial.resolve_left (step0 h1 h3)
   haveI : Fact (Fintype.card N).minFac.Prime := ⟨step4 h1 h3⟩
   exact
-    ⟨⟨fun g h =>
-        eq_top_iff.mp ((step3 h1 h2 h3 (center N)).resolve_left (step6 h1 h2 h3).bot_lt_center.ne')
-          (mem_top h) g⟩⟩
+    ⟨⟨fun g h => ((eq_top_iff.mp ((step3 h1 h2 h3 (center N)).resolve_left
+      (step6 h1 h2 h3).bot_lt_center.ne') (mem_top h)).comm g).symm⟩⟩
 #align subgroup.schur_zassenhaus_induction.step7 Subgroup.SchurZassenhausInduction.step7
 
 end SchurZassenhausInduction

d57133e4

chore: exactly 4 spaces in theorems (#7328)

Co-authored-by: Moritz Firsching <firsching@google.com>

d3263b23

Diff

@@ -97,7 +97,7 @@ theorem smul_diff' (h : H) :
 #align subgroup.smul_diff' Subgroup.smul_diff'
 
 theorem eq_one_of_smul_eq_one (hH : Nat.Coprime (Nat.card H) H.index) (α : H.QuotientDiff)
-  (h : H) : h • α = α → h = 1 :=
+    (h : H) : h • α = α → h = 1 :=
   Quotient.inductionOn' α fun α hα =>
     (powCoprime hH).injective <|
       calc

d57133e4

chore: bump to v4.1.0-rc1 (2nd attempt) (#7216)

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

bfaffcf1

Diff

@@ -96,7 +96,7 @@ theorem smul_diff' (h : H) :
   exact self_eq_mul_right.mpr ((QuotientGroup.eq_one_iff _).mpr h.2)
 #align subgroup.smul_diff' Subgroup.smul_diff'
 
-theorem eq_one_of_smul_eq_one (hH : Nat.coprime (Nat.card H) H.index) (α : H.QuotientDiff)
+theorem eq_one_of_smul_eq_one (hH : Nat.Coprime (Nat.card H) H.index) (α : H.QuotientDiff)
   (h : H) : h • α = α → h = 1 :=
   Quotient.inductionOn' α fun α hα =>
     (powCoprime hH).injective <|
@@ -107,7 +107,7 @@ theorem eq_one_of_smul_eq_one (hH : Nat.coprime (Nat.card H) H.index) (α : H.Qu
 
 #align subgroup.eq_one_of_smul_eq_one Subgroup.eq_one_of_smul_eq_one
 
-theorem exists_smul_eq (hH : Nat.coprime (Nat.card H) H.index) (α β : H.QuotientDiff) :
+theorem exists_smul_eq (hH : Nat.Coprime (Nat.card H) H.index) (α β : H.QuotientDiff) :
     ∃ h : H, h • α = β :=
   Quotient.inductionOn' α
     (Quotient.inductionOn' β fun β α =>
@@ -120,12 +120,12 @@ theorem exists_smul_eq (hH : Nat.coprime (Nat.card H) H.index) (α β : H.Quotie
 #align subgroup.exists_smul_eq Subgroup.exists_smul_eq
 
 theorem isComplement'_stabilizer_of_coprime {α : H.QuotientDiff}
-    (hH : Nat.coprime (Nat.card H) H.index) : IsComplement' H (stabilizer G α) :=
+    (hH : Nat.Coprime (Nat.card H) H.index) : IsComplement' H (stabilizer G α) :=
   isComplement'_stabilizer α (eq_one_of_smul_eq_one hH α) fun g => exists_smul_eq hH (g • α) α
 #align subgroup.is_complement'_stabilizer_of_coprime Subgroup.isComplement'_stabilizer_of_coprime
 
 /-- Do not use this lemma: It is made obsolete by `exists_right_complement'_of_coprime` -/
-private theorem exists_right_complement'_of_coprime_aux (hH : Nat.coprime (Nat.card H) H.index) :
+private theorem exists_right_complement'_of_coprime_aux (hH : Nat.Coprime (Nat.card H) H.index) :
     ∃ K : Subgroup G, IsComplement' H K :=
   instNonempty.elim fun α => ⟨stabilizer G α, isComplement'_stabilizer_of_coprime hH⟩
 
@@ -145,11 +145,11 @@ The proof is by contradiction. We assume that `G` is a minimal counterexample to
 
 
 variable {G : Type u} [Group G] [Fintype G] {N : Subgroup G} [Normal N]
-  (h1 : Nat.coprime (Fintype.card N) N.index)
+  (h1 : Nat.Coprime (Fintype.card N) N.index)
   (h2 :
     ∀ (G' : Type u) [Group G'] [Fintype G'],
       ∀ (_ : Fintype.card G' < Fintype.card G) {N' : Subgroup G'} [N'.Normal]
-        (_ : Nat.coprime (Fintype.card N') N'.index), ∃ H' : Subgroup G', IsComplement' N' H')
+        (_ : Nat.Coprime (Fintype.card N') N'.index), ∃ H' : Subgroup G', IsComplement' N' H')
   (h3 : ∀ H : Subgroup G, ¬IsComplement' N H)
 
 /-! We will arrive at a contradiction via the following steps:
@@ -178,7 +178,7 @@ private theorem step1 (K : Subgroup G) (hK : K ⊔ N = ⊤) : K = ⊤ := by
   have h5 : Fintype.card K < Fintype.card G := by
     rw [← K.index_mul_card]
     exact lt_mul_of_one_lt_left Fintype.card_pos (one_lt_index_of_ne_top h3)
-  have h6 : Nat.coprime (Fintype.card (N.comap K.subtype)) (N.comap K.subtype).index := by
+  have h6 : Nat.Coprime (Fintype.card (N.comap K.subtype)) (N.comap K.subtype).index := by
     rw [h4]
     exact h1.coprime_dvd_left (card_comap_dvd_of_injective N K.subtype Subtype.coe_injective)
   obtain ⟨H, hH⟩ := h2 K h5 h6
@@ -188,7 +188,7 @@ private theorem step1 (K : Subgroup G) (hK : K ⊔ N = ⊤) : K = ⊤ := by
       subtype_range, ←relindex_sup_right, hK, relindex_top_right]
   have h7 : Fintype.card N * Fintype.card (H.map K.subtype) = Fintype.card G := by
     rw [hH, ← N.index_mul_card, mul_comm]
-  have h8 : (Fintype.card N).coprime (Fintype.card (H.map K.subtype)) := by
+  have h8 : (Fintype.card N).Coprime (Fintype.card (H.map K.subtype)) := by
     rwa [hH]
   exact ⟨H.map K.subtype, isComplement'_of_coprime h7 h8⟩
 
@@ -203,7 +203,7 @@ private theorem step2 (K : Subgroup G) [K.Normal] (hK : K ≤ N) : K = ⊥ ∨ K
       lt_mul_of_one_lt_right (Nat.pos_of_ne_zero index_ne_zero_of_finite)
         (K.one_lt_card_iff_ne_bot.mpr h4.1)
   have h6 :
-    (Fintype.card (N.map (QuotientGroup.mk' K))).coprime (N.map (QuotientGroup.mk' K)).index := by
+    (Fintype.card (N.map (QuotientGroup.mk' K))).Coprime (N.map (QuotientGroup.mk' K)).index := by
     have index_map := N.index_map_eq this (by rwa [QuotientGroup.ker_mk'])
     have index_pos : 0 < N.index := Nat.pos_of_ne_zero index_ne_zero_of_finite
     rw [index_map]
@@ -267,7 +267,7 @@ variable {n : ℕ} {G : Type u} [Group G]
 
 /-- Do not use this lemma: It is made obsolete by `exists_right_complement'_of_coprime` -/
 private theorem exists_right_complement'_of_coprime_aux' [Fintype G] (hG : Fintype.card G = n)
-    {N : Subgroup G} [N.Normal] (hN : Nat.coprime (Fintype.card N) N.index) :
+    {N : Subgroup G} [N.Normal] (hN : Nat.Coprime (Fintype.card N) N.index) :
     ∃ H : Subgroup G, IsComplement' N H := by
   revert G
   apply Nat.strongInductionOn n
@@ -281,7 +281,7 @@ private theorem exists_right_complement'_of_coprime_aux' [Fintype G] (hG : Finty
   If `H : Subgroup G` is normal, and has order coprime to its index, then there exists a
   subgroup `K` which is a (right) complement of `H`. -/
 theorem exists_right_complement'_of_coprime_of_fintype [Fintype G] {N : Subgroup G} [N.Normal]
-    (hN : Nat.coprime (Fintype.card N) N.index) : ∃ H : Subgroup G, IsComplement' N H :=
+    (hN : Nat.Coprime (Fintype.card N) N.index) : ∃ H : Subgroup G, IsComplement' N H :=
   exists_right_complement'_of_coprime_aux' rfl hN
 #align subgroup.exists_right_complement'_of_coprime_of_fintype Subgroup.exists_right_complement'_of_coprime_of_fintype
 
@@ -289,7 +289,7 @@ theorem exists_right_complement'_of_coprime_of_fintype [Fintype G] {N : Subgroup
   If `H : Subgroup G` is normal, and has order coprime to its index, then there exists a
   subgroup `K` which is a (right) complement of `H`. -/
 theorem exists_right_complement'_of_coprime {N : Subgroup G} [N.Normal]
-    (hN : Nat.coprime (Nat.card N) N.index) : ∃ H : Subgroup G, IsComplement' N H := by
+    (hN : Nat.Coprime (Nat.card N) N.index) : ∃ H : Subgroup G, IsComplement' N H := by
   by_cases hN1 : Nat.card N = 0
   · rw [hN1, Nat.coprime_zero_left, index_eq_one] at hN
     rw [hN]
@@ -312,7 +312,7 @@ theorem exists_right_complement'_of_coprime {N : Subgroup G} [N.Normal]
   If `H : Subgroup G` is normal, and has order coprime to its index, then there exists a
   subgroup `K` which is a (left) complement of `H`. -/
 theorem exists_left_complement'_of_coprime_of_fintype [Fintype G] {N : Subgroup G} [N.Normal]
-    (hN : Nat.coprime (Fintype.card N) N.index) : ∃ H : Subgroup G, IsComplement' H N :=
+    (hN : Nat.Coprime (Fintype.card N) N.index) : ∃ H : Subgroup G, IsComplement' H N :=
   Exists.imp (fun _ => IsComplement'.symm) (exists_right_complement'_of_coprime_of_fintype hN)
 #align subgroup.exists_left_complement'_of_coprime_of_fintype Subgroup.exists_left_complement'_of_coprime_of_fintype
 
@@ -320,7 +320,7 @@ theorem exists_left_complement'_of_coprime_of_fintype [Fintype G] {N : Subgroup
   If `H : Subgroup G` is normal, and has order coprime to its index, then there exists a
   subgroup `K` which is a (left) complement of `H`. -/
 theorem exists_left_complement'_of_coprime {N : Subgroup G} [N.Normal]
-    (hN : Nat.coprime (Nat.card N) N.index) : ∃ H : Subgroup G, IsComplement' H N :=
+    (hN : Nat.Coprime (Nat.card N) N.index) : ∃ H : Subgroup G, IsComplement' H N :=
   Exists.imp (fun _ => IsComplement'.symm) (exists_right_complement'_of_coprime hN)
 #align subgroup.exists_left_complement'_of_coprime Subgroup.exists_left_complement'_of_coprime

d57133e4

Revert "chore: bump to v4.1.0-rc1 (#7174)" (#7198)

This reverts commit 6f8e8104. Unfortunately this bump was not linted correctly, as CI did not run runLinter Mathlib.

We can unrevert once that's fixed.

40b58304

Diff

@@ -96,7 +96,7 @@ theorem smul_diff' (h : H) :
   exact self_eq_mul_right.mpr ((QuotientGroup.eq_one_iff _).mpr h.2)
 #align subgroup.smul_diff' Subgroup.smul_diff'
 
-theorem eq_one_of_smul_eq_one (hH : Nat.Coprime (Nat.card H) H.index) (α : H.QuotientDiff)
+theorem eq_one_of_smul_eq_one (hH : Nat.coprime (Nat.card H) H.index) (α : H.QuotientDiff)
   (h : H) : h • α = α → h = 1 :=
   Quotient.inductionOn' α fun α hα =>
     (powCoprime hH).injective <|
@@ -107,7 +107,7 @@ theorem eq_one_of_smul_eq_one (hH : Nat.Coprime (Nat.card H) H.index) (α : H.Qu
 
 #align subgroup.eq_one_of_smul_eq_one Subgroup.eq_one_of_smul_eq_one
 
-theorem exists_smul_eq (hH : Nat.Coprime (Nat.card H) H.index) (α β : H.QuotientDiff) :
+theorem exists_smul_eq (hH : Nat.coprime (Nat.card H) H.index) (α β : H.QuotientDiff) :
     ∃ h : H, h • α = β :=
   Quotient.inductionOn' α
     (Quotient.inductionOn' β fun β α =>
@@ -120,12 +120,12 @@ theorem exists_smul_eq (hH : Nat.Coprime (Nat.card H) H.index) (α β : H.Quotie
 #align subgroup.exists_smul_eq Subgroup.exists_smul_eq
 
 theorem isComplement'_stabilizer_of_coprime {α : H.QuotientDiff}
-    (hH : Nat.Coprime (Nat.card H) H.index) : IsComplement' H (stabilizer G α) :=
+    (hH : Nat.coprime (Nat.card H) H.index) : IsComplement' H (stabilizer G α) :=
   isComplement'_stabilizer α (eq_one_of_smul_eq_one hH α) fun g => exists_smul_eq hH (g • α) α
 #align subgroup.is_complement'_stabilizer_of_coprime Subgroup.isComplement'_stabilizer_of_coprime
 
 /-- Do not use this lemma: It is made obsolete by `exists_right_complement'_of_coprime` -/
-private theorem exists_right_complement'_of_coprime_aux (hH : Nat.Coprime (Nat.card H) H.index) :
+private theorem exists_right_complement'_of_coprime_aux (hH : Nat.coprime (Nat.card H) H.index) :
     ∃ K : Subgroup G, IsComplement' H K :=
   instNonempty.elim fun α => ⟨stabilizer G α, isComplement'_stabilizer_of_coprime hH⟩
 
@@ -145,11 +145,11 @@ The proof is by contradiction. We assume that `G` is a minimal counterexample to
 
 
 variable {G : Type u} [Group G] [Fintype G] {N : Subgroup G} [Normal N]
-  (h1 : Nat.Coprime (Fintype.card N) N.index)
+  (h1 : Nat.coprime (Fintype.card N) N.index)
   (h2 :
     ∀ (G' : Type u) [Group G'] [Fintype G'],
       ∀ (_ : Fintype.card G' < Fintype.card G) {N' : Subgroup G'} [N'.Normal]
-        (_ : Nat.Coprime (Fintype.card N') N'.index), ∃ H' : Subgroup G', IsComplement' N' H')
+        (_ : Nat.coprime (Fintype.card N') N'.index), ∃ H' : Subgroup G', IsComplement' N' H')
   (h3 : ∀ H : Subgroup G, ¬IsComplement' N H)
 
 /-! We will arrive at a contradiction via the following steps:
@@ -178,7 +178,7 @@ private theorem step1 (K : Subgroup G) (hK : K ⊔ N = ⊤) : K = ⊤ := by
   have h5 : Fintype.card K < Fintype.card G := by
     rw [← K.index_mul_card]
     exact lt_mul_of_one_lt_left Fintype.card_pos (one_lt_index_of_ne_top h3)
-  have h6 : Nat.Coprime (Fintype.card (N.comap K.subtype)) (N.comap K.subtype).index := by
+  have h6 : Nat.coprime (Fintype.card (N.comap K.subtype)) (N.comap K.subtype).index := by
     rw [h4]
     exact h1.coprime_dvd_left (card_comap_dvd_of_injective N K.subtype Subtype.coe_injective)
   obtain ⟨H, hH⟩ := h2 K h5 h6
@@ -188,7 +188,7 @@ private theorem step1 (K : Subgroup G) (hK : K ⊔ N = ⊤) : K = ⊤ := by
       subtype_range, ←relindex_sup_right, hK, relindex_top_right]
   have h7 : Fintype.card N * Fintype.card (H.map K.subtype) = Fintype.card G := by
     rw [hH, ← N.index_mul_card, mul_comm]
-  have h8 : (Fintype.card N).Coprime (Fintype.card (H.map K.subtype)) := by
+  have h8 : (Fintype.card N).coprime (Fintype.card (H.map K.subtype)) := by
     rwa [hH]
   exact ⟨H.map K.subtype, isComplement'_of_coprime h7 h8⟩
 
@@ -203,7 +203,7 @@ private theorem step2 (K : Subgroup G) [K.Normal] (hK : K ≤ N) : K = ⊥ ∨ K
       lt_mul_of_one_lt_right (Nat.pos_of_ne_zero index_ne_zero_of_finite)
         (K.one_lt_card_iff_ne_bot.mpr h4.1)
   have h6 :
-    (Fintype.card (N.map (QuotientGroup.mk' K))).Coprime (N.map (QuotientGroup.mk' K)).index := by
+    (Fintype.card (N.map (QuotientGroup.mk' K))).coprime (N.map (QuotientGroup.mk' K)).index := by
     have index_map := N.index_map_eq this (by rwa [QuotientGroup.ker_mk'])
     have index_pos : 0 < N.index := Nat.pos_of_ne_zero index_ne_zero_of_finite
     rw [index_map]
@@ -267,7 +267,7 @@ variable {n : ℕ} {G : Type u} [Group G]
 
 /-- Do not use this lemma: It is made obsolete by `exists_right_complement'_of_coprime` -/
 private theorem exists_right_complement'_of_coprime_aux' [Fintype G] (hG : Fintype.card G = n)
-    {N : Subgroup G} [N.Normal] (hN : Nat.Coprime (Fintype.card N) N.index) :
+    {N : Subgroup G} [N.Normal] (hN : Nat.coprime (Fintype.card N) N.index) :
     ∃ H : Subgroup G, IsComplement' N H := by
   revert G
   apply Nat.strongInductionOn n
@@ -281,7 +281,7 @@ private theorem exists_right_complement'_of_coprime_aux' [Fintype G] (hG : Finty
   If `H : Subgroup G` is normal, and has order coprime to its index, then there exists a
   subgroup `K` which is a (right) complement of `H`. -/
 theorem exists_right_complement'_of_coprime_of_fintype [Fintype G] {N : Subgroup G} [N.Normal]
-    (hN : Nat.Coprime (Fintype.card N) N.index) : ∃ H : Subgroup G, IsComplement' N H :=
+    (hN : Nat.coprime (Fintype.card N) N.index) : ∃ H : Subgroup G, IsComplement' N H :=
   exists_right_complement'_of_coprime_aux' rfl hN
 #align subgroup.exists_right_complement'_of_coprime_of_fintype Subgroup.exists_right_complement'_of_coprime_of_fintype
 
@@ -289,7 +289,7 @@ theorem exists_right_complement'_of_coprime_of_fintype [Fintype G] {N : Subgroup
   If `H : Subgroup G` is normal, and has order coprime to its index, then there exists a
   subgroup `K` which is a (right) complement of `H`. -/
 theorem exists_right_complement'_of_coprime {N : Subgroup G} [N.Normal]
-    (hN : Nat.Coprime (Nat.card N) N.index) : ∃ H : Subgroup G, IsComplement' N H := by
+    (hN : Nat.coprime (Nat.card N) N.index) : ∃ H : Subgroup G, IsComplement' N H := by
   by_cases hN1 : Nat.card N = 0
   · rw [hN1, Nat.coprime_zero_left, index_eq_one] at hN
     rw [hN]
@@ -312,7 +312,7 @@ theorem exists_right_complement'_of_coprime {N : Subgroup G} [N.Normal]
   If `H : Subgroup G` is normal, and has order coprime to its index, then there exists a
   subgroup `K` which is a (left) complement of `H`. -/
 theorem exists_left_complement'_of_coprime_of_fintype [Fintype G] {N : Subgroup G} [N.Normal]
-    (hN : Nat.Coprime (Fintype.card N) N.index) : ∃ H : Subgroup G, IsComplement' H N :=
+    (hN : Nat.coprime (Fintype.card N) N.index) : ∃ H : Subgroup G, IsComplement' H N :=
   Exists.imp (fun _ => IsComplement'.symm) (exists_right_complement'_of_coprime_of_fintype hN)
 #align subgroup.exists_left_complement'_of_coprime_of_fintype Subgroup.exists_left_complement'_of_coprime_of_fintype
 
@@ -320,7 +320,7 @@ theorem exists_left_complement'_of_coprime_of_fintype [Fintype G] {N : Subgroup
   If `H : Subgroup G` is normal, and has order coprime to its index, then there exists a
   subgroup `K` which is a (left) complement of `H`. -/
 theorem exists_left_complement'_of_coprime {N : Subgroup G} [N.Normal]
-    (hN : Nat.Coprime (Nat.card N) N.index) : ∃ H : Subgroup G, IsComplement' H N :=
+    (hN : Nat.coprime (Nat.card N) N.index) : ∃ H : Subgroup G, IsComplement' H N :=
   Exists.imp (fun _ => IsComplement'.symm) (exists_right_complement'_of_coprime hN)
 #align subgroup.exists_left_complement'_of_coprime Subgroup.exists_left_complement'_of_coprime

d57133e4

chore: bump to v4.1.0-rc1 (#7174)

Some changes have already been review and delegated in #6910 and #7148.

The diff that needs looking at is https://github.com/leanprover-community/mathlib4/pull/7174/commits/64d6d07ee18163627c8f517eb31455411921c5ac

The std bump PR was insta-merged already!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

6f8e8104

Diff

@@ -96,7 +96,7 @@ theorem smul_diff' (h : H) :
   exact self_eq_mul_right.mpr ((QuotientGroup.eq_one_iff _).mpr h.2)
 #align subgroup.smul_diff' Subgroup.smul_diff'
 
-theorem eq_one_of_smul_eq_one (hH : Nat.coprime (Nat.card H) H.index) (α : H.QuotientDiff)
+theorem eq_one_of_smul_eq_one (hH : Nat.Coprime (Nat.card H) H.index) (α : H.QuotientDiff)
   (h : H) : h • α = α → h = 1 :=
   Quotient.inductionOn' α fun α hα =>
     (powCoprime hH).injective <|
@@ -107,7 +107,7 @@ theorem eq_one_of_smul_eq_one (hH : Nat.coprime (Nat.card H) H.index) (α : H.Qu
 
 #align subgroup.eq_one_of_smul_eq_one Subgroup.eq_one_of_smul_eq_one
 
-theorem exists_smul_eq (hH : Nat.coprime (Nat.card H) H.index) (α β : H.QuotientDiff) :
+theorem exists_smul_eq (hH : Nat.Coprime (Nat.card H) H.index) (α β : H.QuotientDiff) :
     ∃ h : H, h • α = β :=
   Quotient.inductionOn' α
     (Quotient.inductionOn' β fun β α =>
@@ -120,12 +120,12 @@ theorem exists_smul_eq (hH : Nat.coprime (Nat.card H) H.index) (α β : H.Quotie
 #align subgroup.exists_smul_eq Subgroup.exists_smul_eq
 
 theorem isComplement'_stabilizer_of_coprime {α : H.QuotientDiff}
-    (hH : Nat.coprime (Nat.card H) H.index) : IsComplement' H (stabilizer G α) :=
+    (hH : Nat.Coprime (Nat.card H) H.index) : IsComplement' H (stabilizer G α) :=
   isComplement'_stabilizer α (eq_one_of_smul_eq_one hH α) fun g => exists_smul_eq hH (g • α) α
 #align subgroup.is_complement'_stabilizer_of_coprime Subgroup.isComplement'_stabilizer_of_coprime
 
 /-- Do not use this lemma: It is made obsolete by `exists_right_complement'_of_coprime` -/
-private theorem exists_right_complement'_of_coprime_aux (hH : Nat.coprime (Nat.card H) H.index) :
+private theorem exists_right_complement'_of_coprime_aux (hH : Nat.Coprime (Nat.card H) H.index) :
     ∃ K : Subgroup G, IsComplement' H K :=
   instNonempty.elim fun α => ⟨stabilizer G α, isComplement'_stabilizer_of_coprime hH⟩
 
@@ -145,11 +145,11 @@ The proof is by contradiction. We assume that `G` is a minimal counterexample to
 
 
 variable {G : Type u} [Group G] [Fintype G] {N : Subgroup G} [Normal N]
-  (h1 : Nat.coprime (Fintype.card N) N.index)
+  (h1 : Nat.Coprime (Fintype.card N) N.index)
   (h2 :
     ∀ (G' : Type u) [Group G'] [Fintype G'],
       ∀ (_ : Fintype.card G' < Fintype.card G) {N' : Subgroup G'} [N'.Normal]
-        (_ : Nat.coprime (Fintype.card N') N'.index), ∃ H' : Subgroup G', IsComplement' N' H')
+        (_ : Nat.Coprime (Fintype.card N') N'.index), ∃ H' : Subgroup G', IsComplement' N' H')
   (h3 : ∀ H : Subgroup G, ¬IsComplement' N H)
 
 /-! We will arrive at a contradiction via the following steps:
@@ -178,7 +178,7 @@ private theorem step1 (K : Subgroup G) (hK : K ⊔ N = ⊤) : K = ⊤ := by
   have h5 : Fintype.card K < Fintype.card G := by
     rw [← K.index_mul_card]
     exact lt_mul_of_one_lt_left Fintype.card_pos (one_lt_index_of_ne_top h3)
-  have h6 : Nat.coprime (Fintype.card (N.comap K.subtype)) (N.comap K.subtype).index := by
+  have h6 : Nat.Coprime (Fintype.card (N.comap K.subtype)) (N.comap K.subtype).index := by
     rw [h4]
     exact h1.coprime_dvd_left (card_comap_dvd_of_injective N K.subtype Subtype.coe_injective)
   obtain ⟨H, hH⟩ := h2 K h5 h6
@@ -188,7 +188,7 @@ private theorem step1 (K : Subgroup G) (hK : K ⊔ N = ⊤) : K = ⊤ := by
       subtype_range, ←relindex_sup_right, hK, relindex_top_right]
   have h7 : Fintype.card N * Fintype.card (H.map K.subtype) = Fintype.card G := by
     rw [hH, ← N.index_mul_card, mul_comm]
-  have h8 : (Fintype.card N).coprime (Fintype.card (H.map K.subtype)) := by
+  have h8 : (Fintype.card N).Coprime (Fintype.card (H.map K.subtype)) := by
     rwa [hH]
   exact ⟨H.map K.subtype, isComplement'_of_coprime h7 h8⟩
 
@@ -203,7 +203,7 @@ private theorem step2 (K : Subgroup G) [K.Normal] (hK : K ≤ N) : K = ⊥ ∨ K
       lt_mul_of_one_lt_right (Nat.pos_of_ne_zero index_ne_zero_of_finite)
         (K.one_lt_card_iff_ne_bot.mpr h4.1)
   have h6 :
-    (Fintype.card (N.map (QuotientGroup.mk' K))).coprime (N.map (QuotientGroup.mk' K)).index := by
+    (Fintype.card (N.map (QuotientGroup.mk' K))).Coprime (N.map (QuotientGroup.mk' K)).index := by
     have index_map := N.index_map_eq this (by rwa [QuotientGroup.ker_mk'])
     have index_pos : 0 < N.index := Nat.pos_of_ne_zero index_ne_zero_of_finite
     rw [index_map]
@@ -267,7 +267,7 @@ variable {n : ℕ} {G : Type u} [Group G]
 
 /-- Do not use this lemma: It is made obsolete by `exists_right_complement'_of_coprime` -/
 private theorem exists_right_complement'_of_coprime_aux' [Fintype G] (hG : Fintype.card G = n)
-    {N : Subgroup G} [N.Normal] (hN : Nat.coprime (Fintype.card N) N.index) :
+    {N : Subgroup G} [N.Normal] (hN : Nat.Coprime (Fintype.card N) N.index) :
     ∃ H : Subgroup G, IsComplement' N H := by
   revert G
   apply Nat.strongInductionOn n
@@ -281,7 +281,7 @@ private theorem exists_right_complement'_of_coprime_aux' [Fintype G] (hG : Finty
   If `H : Subgroup G` is normal, and has order coprime to its index, then there exists a
   subgroup `K` which is a (right) complement of `H`. -/
 theorem exists_right_complement'_of_coprime_of_fintype [Fintype G] {N : Subgroup G} [N.Normal]
-    (hN : Nat.coprime (Fintype.card N) N.index) : ∃ H : Subgroup G, IsComplement' N H :=
+    (hN : Nat.Coprime (Fintype.card N) N.index) : ∃ H : Subgroup G, IsComplement' N H :=
   exists_right_complement'_of_coprime_aux' rfl hN
 #align subgroup.exists_right_complement'_of_coprime_of_fintype Subgroup.exists_right_complement'_of_coprime_of_fintype
 
@@ -289,7 +289,7 @@ theorem exists_right_complement'_of_coprime_of_fintype [Fintype G] {N : Subgroup
   If `H : Subgroup G` is normal, and has order coprime to its index, then there exists a
   subgroup `K` which is a (right) complement of `H`. -/
 theorem exists_right_complement'_of_coprime {N : Subgroup G} [N.Normal]
-    (hN : Nat.coprime (Nat.card N) N.index) : ∃ H : Subgroup G, IsComplement' N H := by
+    (hN : Nat.Coprime (Nat.card N) N.index) : ∃ H : Subgroup G, IsComplement' N H := by
   by_cases hN1 : Nat.card N = 0
   · rw [hN1, Nat.coprime_zero_left, index_eq_one] at hN
     rw [hN]
@@ -312,7 +312,7 @@ theorem exists_right_complement'_of_coprime {N : Subgroup G} [N.Normal]
   If `H : Subgroup G` is normal, and has order coprime to its index, then there exists a
   subgroup `K` which is a (left) complement of `H`. -/
 theorem exists_left_complement'_of_coprime_of_fintype [Fintype G] {N : Subgroup G} [N.Normal]
-    (hN : Nat.coprime (Fintype.card N) N.index) : ∃ H : Subgroup G, IsComplement' H N :=
+    (hN : Nat.Coprime (Fintype.card N) N.index) : ∃ H : Subgroup G, IsComplement' H N :=
   Exists.imp (fun _ => IsComplement'.symm) (exists_right_complement'_of_coprime_of_fintype hN)
 #align subgroup.exists_left_complement'_of_coprime_of_fintype Subgroup.exists_left_complement'_of_coprime_of_fintype
 
@@ -320,7 +320,7 @@ theorem exists_left_complement'_of_coprime_of_fintype [Fintype G] {N : Subgroup
   If `H : Subgroup G` is normal, and has order coprime to its index, then there exists a
   subgroup `K` which is a (left) complement of `H`. -/
 theorem exists_left_complement'_of_coprime {N : Subgroup G} [N.Normal]
-    (hN : Nat.coprime (Nat.card N) N.index) : ∃ H : Subgroup G, IsComplement' H N :=
+    (hN : Nat.Coprime (Nat.card N) N.index) : ∃ H : Subgroup G, IsComplement' H N :=
   Exists.imp (fun _ => IsComplement'.symm) (exists_right_complement'_of_coprime hN)
 #align subgroup.exists_left_complement'_of_coprime Subgroup.exists_left_complement'_of_coprime

d57133e4

chore: remove unused simps (#6632)

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

916c75c1

Diff

@@ -90,7 +90,7 @@ theorem smul_diff' (h : H) :
   letI := H.fintypeQuotientOfFiniteIndex
   rw [diff, diff, index_eq_card, ←Finset.card_univ, ←Finset.prod_const, ←Finset.prod_mul_distrib]
   refine' Finset.prod_congr rfl fun q _ => _
-  simp_rw [Subtype.ext_iff, MonoidHom.id_apply, coe_mul, coe_mk, mul_assoc, mul_right_inj]
+  simp_rw [Subtype.ext_iff, MonoidHom.id_apply, coe_mul, mul_assoc, mul_right_inj]
   rw [smul_apply_eq_smul_apply_inv_smul, smul_eq_mul_unop, unop_op, mul_left_inj, ←Subtype.ext_iff,
     Equiv.apply_eq_iff_eq, inv_smul_eq_iff]
   exact self_eq_mul_right.mpr ((QuotientGroup.eq_one_iff _).mpr h.2)

d57133e4

chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

32de3f67

Diff

@@ -32,7 +32,7 @@ section SchurZassenhausAbelian
 
 open MulOpposite MulAction Subgroup.leftTransversals MemLeftTransversals
 
-variable {G : Type _} [Group G] (H : Subgroup G) [IsCommutative H] [FiniteIndex H]
+variable {G : Type*} [Group G] (H : Subgroup G) [IsCommutative H] [FiniteIndex H]
   (α β : leftTransversals (H : Set G))
 
 /-- The quotient of the transversals of an abelian normal `N` by the `diff` relation. -/

d57133e4

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Thomas Browning. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Thomas Browning
-
-! This file was ported from Lean 3 source module group_theory.schur_zassenhaus
-! leanprover-community/mathlib commit d57133e49cf06508700ef69030cd099917e0f0de
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.GroupTheory.Sylow
 import Mathlib.GroupTheory.Transfer
 
+#align_import group_theory.schur_zassenhaus from "leanprover-community/mathlib"@"d57133e49cf06508700ef69030cd099917e0f0de"
+
 /-!
 # The Schur-Zassenhaus Theorem

d57133e4

chore: cleanup whitespace (#5988)

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

12343aa5

Diff

@@ -21,7 +21,7 @@ In this file we prove the Schur-Zassenhaus theorem.
 - `exists_right_complement'_of_coprime` : The **Schur-Zassenhaus** theorem:
   If `H : Subgroup G` is normal and has order coprime to its index,
   then there exists a subgroup `K` which is a (right) complement of `H`.
-- `exists_left_complement'_of_coprime`  The **Schur-Zassenhaus** theorem:
+- `exists_left_complement'_of_coprime` : The **Schur-Zassenhaus** theorem:
   If `H : Subgroup G` is normal and has order coprime to its index,
   then there exists a subgroup `K` which is a (left) complement of `H`.
 -/

d57133e4

chore: fix align linebreaks (#5683)

The result of running

find . -type f -name "*.lean" -exec sed -i -E 'N;s/^#align ([^[:space:]]+)\n *([^[:space:]]+)$/#align \1 \2/' {} \;

Hopefully for the last time...

Co-authored-by: Moritz Firsching <firsching@google.com>

2a702960

Diff

@@ -286,8 +286,7 @@ private theorem exists_right_complement'_of_coprime_aux' [Fintype G] (hG : Finty
 theorem exists_right_complement'_of_coprime_of_fintype [Fintype G] {N : Subgroup G} [N.Normal]
     (hN : Nat.coprime (Fintype.card N) N.index) : ∃ H : Subgroup G, IsComplement' N H :=
   exists_right_complement'_of_coprime_aux' rfl hN
-#align subgroup.exists_right_complement'_of_coprime_of_fintype
-  Subgroup.exists_right_complement'_of_coprime_of_fintype
+#align subgroup.exists_right_complement'_of_coprime_of_fintype Subgroup.exists_right_complement'_of_coprime_of_fintype
 
 /-- **Schur-Zassenhaus** for normal subgroups:
   If `H : Subgroup G` is normal, and has order coprime to its index, then there exists a
@@ -318,8 +317,7 @@ theorem exists_right_complement'_of_coprime {N : Subgroup G} [N.Normal]
 theorem exists_left_complement'_of_coprime_of_fintype [Fintype G] {N : Subgroup G} [N.Normal]
     (hN : Nat.coprime (Fintype.card N) N.index) : ∃ H : Subgroup G, IsComplement' H N :=
   Exists.imp (fun _ => IsComplement'.symm) (exists_right_complement'_of_coprime_of_fintype hN)
-#align subgroup.exists_left_complement'_of_coprime_of_fintype
-  Subgroup.exists_left_complement'_of_coprime_of_fintype
+#align subgroup.exists_left_complement'_of_coprime_of_fintype Subgroup.exists_left_complement'_of_coprime_of_fintype
 
 /-- **Schur-Zassenhaus** for normal subgroups:
   If `H : Subgroup G` is normal, and has order coprime to its index, then there exists a

d57133e4

fix(Tactic/PushNeg): add cleanupAnnotations to push_neg (#5082)

Exprs now have an mdata field. It seems that this gets in the way of push_neg, as reported on Zulip.

The above seems to fix the reported errors.

Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>

868e361b

Diff

@@ -200,7 +200,6 @@ private theorem step2 (K : Subgroup G) [K.Normal] (hK : K ≤ N) : K = ⊥ ∨ K
   have : Function.Surjective (QuotientGroup.mk' K) := Quotient.surjective_Quotient_mk''
   have h4 := step1 h1 h2 h3
   contrapose! h4
-  rw [not_or] at h4 -- porting note: had to add `rw [not_or] at h4`
   have h5 : Fintype.card (G ⧸ K) < Fintype.card G := by
     rw [← index_eq_card, ← K.index_mul_card]
     refine'

d57133e4

chore: tidy various files (#4854)

5238ba14

Diff

@@ -124,7 +124,7 @@ theorem exists_smul_eq (hH : Nat.coprime (Nat.card H) H.index) (α β : H.Quotie
 
 theorem isComplement'_stabilizer_of_coprime {α : H.QuotientDiff}
     (hH : Nat.coprime (Nat.card H) H.index) : IsComplement' H (stabilizer G α) :=
-  IsComplement'_stabilizer α (eq_one_of_smul_eq_one hH α) fun g => exists_smul_eq hH (g • α) α
+  isComplement'_stabilizer α (eq_one_of_smul_eq_one hH α) fun g => exists_smul_eq hH (g • α) α
 #align subgroup.is_complement'_stabilizer_of_coprime Subgroup.isComplement'_stabilizer_of_coprime
 
 /-- Do not use this lemma: It is made obsolete by `exists_right_complement'_of_coprime` -/
@@ -170,7 +170,7 @@ variable {G : Type u} [Group G] [Fintype G] {N : Subgroup G} [Normal N]
 /-- Do not use this lemma: It is made obsolete by `exists_right_complement'_of_coprime` -/
 private theorem step0 : N ≠ ⊥ := by
   rintro rfl
-  exact h3 ⊤ IsComplement'_bot_top
+  exact h3 ⊤ isComplement'_bot_top
 
 /-- Do not use this lemma: It is made obsolete by `exists_right_complement'_of_coprime` -/
 private theorem step1 (K : Subgroup G) (hK : K ⊔ N = ⊤) : K = ⊤ := by
@@ -193,7 +193,7 @@ private theorem step1 (K : Subgroup G) (hK : K ⊔ N = ⊤) : K = ⊤ := by
     rw [hH, ← N.index_mul_card, mul_comm]
   have h8 : (Fintype.card N).coprime (Fintype.card (H.map K.subtype)) := by
     rwa [hH]
-  exact ⟨H.map K.subtype, IsComplement'_of_coprime h7 h8⟩
+  exact ⟨H.map K.subtype, isComplement'_of_coprime h7 h8⟩
 
 /-- Do not use this lemma: It is made obsolete by `exists_right_complement'_of_coprime` -/
 private theorem step2 (K : Subgroup G) [K.Normal] (hK : K ≤ N) : K = ⊥ ∨ K = N := by
@@ -222,7 +222,7 @@ private theorem step2 (K : Subgroup G) [K.Normal] (hK : K ≤ N) : K = ⊥ ∨ K
     rwa [← key, comap_sup_eq, hH.symm.sup_eq_top, comap_top]
   · rw [← comap_top (QuotientGroup.mk' K)]
     intro hH'
-    rw [comap_injective this hH', IsComplement'_top_right, map_eq_bot_iff,
+    rw [comap_injective this hH', isComplement'_top_right, map_eq_bot_iff,
       QuotientGroup.ker_mk'] at hH
     · exact h4.2 (le_antisymm hK hH)
 
@@ -298,12 +298,12 @@ theorem exists_right_complement'_of_coprime {N : Subgroup G} [N.Normal]
   by_cases hN1 : Nat.card N = 0
   · rw [hN1, Nat.coprime_zero_left, index_eq_one] at hN
     rw [hN]
-    exact ⟨⊥, IsComplement'_top_bot⟩
+    exact ⟨⊥, isComplement'_top_bot⟩
   by_cases hN2 : N.index = 0
   · rw [hN2, Nat.coprime_zero_right] at hN
     haveI := (Cardinal.toNat_eq_one_iff_unique.mp hN).1
     rw [N.eq_bot_of_subsingleton]
-    exact ⟨⊤, IsComplement'_bot_top⟩
+    exact ⟨⊤, isComplement'_bot_top⟩
   have hN3 : Nat.card G ≠ 0 := by
     rw [← N.card_mul_index]
     exact mul_ne_zero hN1 hN2

d57133e4

feat: port GroupTheory.SchurZassenhaus (#4752)

050bf14d

`group_theory.schur_zassenhaus` ⟷ `Mathlib.GroupTheory.SchurZassenhaus`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 541

group_theory.schur_zassenhaus ⟷ Mathlib.GroupTheory.SchurZassenhaus

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 541

`group_theory.schur_zassenhaus` ⟷ `Mathlib.GroupTheory.SchurZassenhaus`