group_theory.transfer | Mathlib porting status

(last sync)

fix(group_theory/subgroup/basic): generalize centralizer from subgroup G to set G (#18965)

This is consistent with all the other sub<foo>.centralizer definitions.

This generalization reveals that a lot of downstream results are rather strangely stated about zpowers. This does not attempt to change these, instead leaving the work for a follow up (either in a later mathlib3 PR or in mathlib4).

Diff

@@ -172,7 +172,7 @@ rfl
 
 section burnside_transfer
 
-variables {p : ℕ} (P : sylow p G) (hP : (P : subgroup G).normalizer ≤ (P : subgroup G).centralizer)
+variables {p : ℕ} (P : sylow p G) (hP : (P : subgroup G).normalizer ≤ centralizer (P : set G))
 
 include hP

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -191,7 +191,7 @@ theorem transfer_eq_pow [FiniteIndex H] (g : G)
     transfer ϕ g = ϕ ⟨g ^ H.index, transfer_eq_pow_aux g key⟩ := by
   classical
   letI := H.fintype_quotient_of_finite_index
-  change ∀ (k g₀) (hk : g₀⁻¹ * g ^ k * g₀ ∈ H), ↑(⟨g₀⁻¹ * g ^ k * g₀, hk⟩ : H) = g ^ k at key 
+  change ∀ (k g₀) (hk : g₀⁻¹ * g ^ k * g₀ ∈ H), ↑(⟨g₀⁻¹ * g ^ k * g₀, hk⟩ : H) = g ^ k at key
   rw [transfer_eq_prod_quotient_orbit_rel_zpowers_quot, ← Finset.prod_to_list, List.prod_map_hom]
   refine' congr_arg ϕ (Subtype.coe_injective _)
   rw [H.coe_mk, ← (zpowers g).coe_mk g (mem_zpowers g), ← (zpowers g).coe_pow, (zpowers g).coe_mk,
@@ -287,11 +287,11 @@ theorem ker_transferSylow_isComplement' : IsComplement' (transferSylow P hP).ker
       (P.2.powEquiv'
           (not_dvd_index_sylow P
             (mt index_eq_zero_of_relindex_eq_zero index_ne_zero_of_finite))).Bijective
-  rw [Function.Bijective, ← range_top_iff_surjective, restrict_range] at hf 
+  rw [Function.Bijective, ← range_top_iff_surjective, restrict_range] at hf
   have := range_top_iff_surjective.mp (top_le_iff.mp (hf.2.ge.trans (map_le_range _ P)))
   rw [← (comap_injective this).eq_iff, comap_top, comap_map_eq, sup_comm, SetLike.ext'_iff,
     normal_mul, ← ker_eq_bot_iff, ← (map_injective (P : Subgroup G).subtype_injective).eq_iff,
-    ker_restrict, subgroup_of_map_subtype, Subgroup.map_bot, coe_top] at hf 
+    ker_restrict, subgroup_of_map_subtype, Subgroup.map_bot, coe_top] at hf
   exact is_complement'_of_disjoint_and_mul_eq_univ (disjoint_iff.2 hf.1) hf.2
 #align monoid_hom.ker_transfer_sylow_is_complement' MonoidHom.ker_transferSylow_isComplement'
 -/

bump to nightly-2024-02-23-08

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

ac9421d6

Diff

@@ -254,8 +254,7 @@ variable [Fact p.Prime] [Finite (Sylow p G)]
 theorem transferSylow_eq_pow_aux (g : G) (hg : g ∈ P) (k : ℕ) (g₀ : G) (h : g₀⁻¹ * g ^ k * g₀ ∈ P) :
     g₀⁻¹ * g ^ k * g₀ = g ^ k :=
   by
-  haveI : (P : Subgroup G).IsCommutativeₓ :=
-    ⟨⟨fun a b => Subtype.ext (hP (le_normalizer b.2) a a.2)⟩⟩
+  haveI : (P : Subgroup G).Commutative := ⟨⟨fun a b => Subtype.ext (hP (le_normalizer b.2) a a.2)⟩⟩
   replace hg := (P : Subgroup G).pow_mem hg k
   obtain ⟨n, hn, h⟩ := P.conj_eq_normalizer_conj_of_mem (g ^ k) g₀ hg h
   exact h.trans (Commute.inv_mul_cancel (hP hn (g ^ k) hg).symm)

bump to nightly-2024-02-05-08

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

516c6ec2

Diff

@@ -254,7 +254,7 @@ variable [Fact p.Prime] [Finite (Sylow p G)]
 theorem transferSylow_eq_pow_aux (g : G) (hg : g ∈ P) (k : ℕ) (g₀ : G) (h : g₀⁻¹ * g ^ k * g₀ ∈ P) :
     g₀⁻¹ * g ^ k * g₀ = g ^ k :=
   by
-  haveI : (P : Subgroup G).IsCommutative :=
+  haveI : (P : Subgroup G).IsCommutativeₓ :=
     ⟨⟨fun a b => Subtype.ext (hP (le_normalizer b.2) a a.2)⟩⟩
   replace hg := (P : Subgroup G).pow_mem hg k
   obtain ⟨n, hn, h⟩ := P.conj_eq_normalizer_conj_of_mem (g ^ k) g₀ hg h

bump to nightly-2024-02-01-06

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

5433bded

Diff

@@ -144,7 +144,20 @@ theorem transfer_eq_prod_quotient_orbitRel_zpowers_quot [FiniteIndex H] (g : G)
         ϕ
           ⟨q.out'.out'⁻¹ * g ^ Function.minimalPeriod ((· • ·) g) q.out' * q.out'.out',
             QuotientGroup.out'_conj_pow_minimalPeriod_mem H g q.out'⟩ :=
-  by classical
+  by
+  classical
+  letI := H.fintype_quotient_of_finite_index
+  calc
+    transfer ϕ g = ∏ q : G ⧸ H, _ := transfer_def ϕ (transfer_transversal H g) g
+    _ = _ := ((quotient_equiv_sigma_zmod H g).symm.prod_comp _).symm
+    _ = _ := (Finset.prod_sigma _ _ _)
+    _ = _ := Fintype.prod_congr _ _ fun q => _
+  simp only [quotient_equiv_sigma_zmod_symm_apply, transfer_transversal_apply',
+    transfer_transversal_apply'']
+  rw [Fintype.prod_eq_single (0 : ZMod (Function.minimalPeriod ((· • ·) g) q.out')) fun k hk => _]
+  · simp only [if_pos, ZMod.cast_zero, zpow_zero, one_mul, mul_assoc]
+  · simp only [if_neg hk, inv_mul_self]
+    exact map_one ϕ
 #align monoid_hom.transfer_eq_prod_quotient_orbit_rel_zpowers_quot MonoidHom.transfer_eq_prod_quotient_orbitRel_zpowers_quot
 -/
 
@@ -158,13 +171,36 @@ theorem transfer_eq_pow_aux (g : G)
     exact H.one_mem
   letI := fintype_of_index_ne_zero hH
   classical
+  replace key : ∀ (k : ℕ) (g₀ : G), g₀⁻¹ * g ^ k * g₀ ∈ H → g ^ k ∈ H := fun k g₀ hk =>
+    (_root_.congr_arg (· ∈ H) (key k g₀ hk)).mp hk
+  replace key : ∀ q : G ⧸ H, g ^ Function.minimalPeriod ((· • ·) g) q ∈ H := fun q =>
+    key (Function.minimalPeriod ((· • ·) g) q) q.out'
+      (QuotientGroup.out'_conj_pow_minimalPeriod_mem H g q)
+  let f : Quotient (orbit_rel (zpowers g) (G ⧸ H)) → zpowers g := fun q =>
+    (⟨g, mem_zpowers g⟩ : zpowers g) ^ Function.minimalPeriod ((· • ·) g) q.out'
+  have hf : ∀ q, f q ∈ H.subgroup_of (zpowers g) := fun q => key q.out'
+  replace key := Subgroup.prod_mem (H.subgroup_of (zpowers g)) fun q (hq : q ∈ Finset.univ) => hf q
+  simpa only [minimal_period_eq_card, Finset.prod_pow_eq_pow_sum, Fintype.card_sigma,
+    Fintype.card_congr (self_equiv_sigma_orbits (zpowers g) (G ⧸ H)), index_eq_card] using key
 #align monoid_hom.transfer_eq_pow_aux MonoidHom.transfer_eq_pow_aux
 -/
 
 #print MonoidHom.transfer_eq_pow /-
 theorem transfer_eq_pow [FiniteIndex H] (g : G)
     (key : ∀ (k : ℕ) (g₀ : G), g₀⁻¹ * g ^ k * g₀ ∈ H → g₀⁻¹ * g ^ k * g₀ = g ^ k) :
-    transfer ϕ g = ϕ ⟨g ^ H.index, transfer_eq_pow_aux g key⟩ := by classical
+    transfer ϕ g = ϕ ⟨g ^ H.index, transfer_eq_pow_aux g key⟩ := by
+  classical
+  letI := H.fintype_quotient_of_finite_index
+  change ∀ (k g₀) (hk : g₀⁻¹ * g ^ k * g₀ ∈ H), ↑(⟨g₀⁻¹ * g ^ k * g₀, hk⟩ : H) = g ^ k at key 
+  rw [transfer_eq_prod_quotient_orbit_rel_zpowers_quot, ← Finset.prod_to_list, List.prod_map_hom]
+  refine' congr_arg ϕ (Subtype.coe_injective _)
+  rw [H.coe_mk, ← (zpowers g).coe_mk g (mem_zpowers g), ← (zpowers g).coe_pow, (zpowers g).coe_mk,
+    index_eq_card, Fintype.card_congr (self_equiv_sigma_orbits (zpowers g) (G ⧸ H)),
+    Fintype.card_sigma, ← Finset.prod_pow_eq_pow_sum, ← Finset.prod_to_list]
+  simp only [coe_list_prod, List.map_map, ← minimal_period_eq_card]
+  congr 2
+  funext
+  apply key
 #align monoid_hom.transfer_eq_pow MonoidHom.transfer_eq_pow
 -/

bump to nightly-2024-01-31-06

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

61100fe9

Diff

@@ -144,20 +144,7 @@ theorem transfer_eq_prod_quotient_orbitRel_zpowers_quot [FiniteIndex H] (g : G)
         ϕ
           ⟨q.out'.out'⁻¹ * g ^ Function.minimalPeriod ((· • ·) g) q.out' * q.out'.out',
             QuotientGroup.out'_conj_pow_minimalPeriod_mem H g q.out'⟩ :=
-  by
-  classical
-  letI := H.fintype_quotient_of_finite_index
-  calc
-    transfer ϕ g = ∏ q : G ⧸ H, _ := transfer_def ϕ (transfer_transversal H g) g
-    _ = _ := ((quotient_equiv_sigma_zmod H g).symm.prod_comp _).symm
-    _ = _ := (Finset.prod_sigma _ _ _)
-    _ = _ := Fintype.prod_congr _ _ fun q => _
-  simp only [quotient_equiv_sigma_zmod_symm_apply, transfer_transversal_apply',
-    transfer_transversal_apply'']
-  rw [Fintype.prod_eq_single (0 : ZMod (Function.minimalPeriod ((· • ·) g) q.out')) fun k hk => _]
-  · simp only [if_pos, ZMod.cast_zero, zpow_zero, one_mul, mul_assoc]
-  · simp only [if_neg hk, inv_mul_self]
-    exact map_one ϕ
+  by classical
 #align monoid_hom.transfer_eq_prod_quotient_orbit_rel_zpowers_quot MonoidHom.transfer_eq_prod_quotient_orbitRel_zpowers_quot
 -/
 
@@ -171,36 +158,13 @@ theorem transfer_eq_pow_aux (g : G)
     exact H.one_mem
   letI := fintype_of_index_ne_zero hH
   classical
-  replace key : ∀ (k : ℕ) (g₀ : G), g₀⁻¹ * g ^ k * g₀ ∈ H → g ^ k ∈ H := fun k g₀ hk =>
-    (_root_.congr_arg (· ∈ H) (key k g₀ hk)).mp hk
-  replace key : ∀ q : G ⧸ H, g ^ Function.minimalPeriod ((· • ·) g) q ∈ H := fun q =>
-    key (Function.minimalPeriod ((· • ·) g) q) q.out'
-      (QuotientGroup.out'_conj_pow_minimalPeriod_mem H g q)
-  let f : Quotient (orbit_rel (zpowers g) (G ⧸ H)) → zpowers g := fun q =>
-    (⟨g, mem_zpowers g⟩ : zpowers g) ^ Function.minimalPeriod ((· • ·) g) q.out'
-  have hf : ∀ q, f q ∈ H.subgroup_of (zpowers g) := fun q => key q.out'
-  replace key := Subgroup.prod_mem (H.subgroup_of (zpowers g)) fun q (hq : q ∈ Finset.univ) => hf q
-  simpa only [minimal_period_eq_card, Finset.prod_pow_eq_pow_sum, Fintype.card_sigma,
-    Fintype.card_congr (self_equiv_sigma_orbits (zpowers g) (G ⧸ H)), index_eq_card] using key
 #align monoid_hom.transfer_eq_pow_aux MonoidHom.transfer_eq_pow_aux
 -/
 
 #print MonoidHom.transfer_eq_pow /-
 theorem transfer_eq_pow [FiniteIndex H] (g : G)
     (key : ∀ (k : ℕ) (g₀ : G), g₀⁻¹ * g ^ k * g₀ ∈ H → g₀⁻¹ * g ^ k * g₀ = g ^ k) :
-    transfer ϕ g = ϕ ⟨g ^ H.index, transfer_eq_pow_aux g key⟩ := by
-  classical
-  letI := H.fintype_quotient_of_finite_index
-  change ∀ (k g₀) (hk : g₀⁻¹ * g ^ k * g₀ ∈ H), ↑(⟨g₀⁻¹ * g ^ k * g₀, hk⟩ : H) = g ^ k at key 
-  rw [transfer_eq_prod_quotient_orbit_rel_zpowers_quot, ← Finset.prod_to_list, List.prod_map_hom]
-  refine' congr_arg ϕ (Subtype.coe_injective _)
-  rw [H.coe_mk, ← (zpowers g).coe_mk g (mem_zpowers g), ← (zpowers g).coe_pow, (zpowers g).coe_mk,
-    index_eq_card, Fintype.card_congr (self_equiv_sigma_orbits (zpowers g) (G ⧸ H)),
-    Fintype.card_sigma, ← Finset.prod_pow_eq_pow_sum, ← Finset.prod_to_list]
-  simp only [coe_list_prod, List.map_map, ← minimal_period_eq_card]
-  congr 2
-  funext
-  apply key
+    transfer ϕ g = ϕ ⟨g ^ H.index, transfer_eq_pow_aux g key⟩ := by classical
 #align monoid_hom.transfer_eq_pow MonoidHom.transfer_eq_pow
 -/

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) 2022 Thomas Browning. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Thomas Browning
 -/
-import Mathbin.GroupTheory.Complement
-import Mathbin.GroupTheory.Sylow
+import GroupTheory.Complement
+import GroupTheory.Sylow
 
 #align_import group_theory.transfer from "leanprover-community/mathlib"@"4be589053caf347b899a494da75410deb55fb3ef"

bump to nightly-2023-08-17-09

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

60285dcc

Diff

@@ -64,7 +64,7 @@ noncomputable def diff : A :=
 theorem diff_mul_diff : diff ϕ R S * diff ϕ S T = diff ϕ R T :=
   prod_mul_distrib.symm.trans
     (prod_congr rfl fun q hq =>
-      (ϕ.map_mul _ _).symm.trans
+      (ϕ.map_hMul _ _).symm.trans
         (congr_arg ϕ
           (by simp_rw [Subtype.ext_iff, coe_mul, coe_mk, mul_assoc, mul_inv_cancel_left])))
 #align subgroup.left_transversals.diff_mul_diff Subgroup.leftTransversals.diff_mul_diff

bump to nightly-2023-07-25-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/c0c52abb75074ed8b73a948341f50521fbf43b4c

748c9a7c

Diff

@@ -6,7 +6,7 @@ Authors: Thomas Browning
 import Mathbin.GroupTheory.Complement
 import Mathbin.GroupTheory.Sylow
 
-#align_import group_theory.transfer from "leanprover-community/mathlib"@"36938f775671ff28bea1c0310f1608e4afbb22e0"
+#align_import group_theory.transfer from "leanprover-community/mathlib"@"4be589053caf347b899a494da75410deb55fb3ef"
 
 /-!
 # The Transfer Homomorphism
@@ -235,7 +235,7 @@ theorem transferCenterPow_apply [FiniteIndex (center G)] (g : G) :
 
 section BurnsideTransfer
 
-variable {p : ℕ} (P : Sylow p G) (hP : (P : Subgroup G).normalizer ≤ (P : Subgroup G).centralizer)
+variable {p : ℕ} (P : Sylow p G) (hP : (P : Subgroup G).normalizer ≤ centralizer (P : Set G))
 
 #print MonoidHom.transferSylow /-
 /-- The homomorphism `G →* P` in Burnside's transfer theorem. -/

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) 2022 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.transfer
-! leanprover-community/mathlib commit 36938f775671ff28bea1c0310f1608e4afbb22e0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.GroupTheory.Complement
 import Mathbin.GroupTheory.Sylow
 
+#align_import group_theory.transfer from "leanprover-community/mathlib"@"36938f775671ff28bea1c0310f1608e4afbb22e0"
+
 /-!
 # The Transfer Homomorphism

bump to nightly-2023-06-18-23

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

3b5e23dc

Diff

@@ -252,17 +252,17 @@ noncomputable def transferSylow [FiniteIndex (P : Subgroup G)] : G →* (P : Sub
 
 variable [Fact p.Prime] [Finite (Sylow p G)]
 
-#print MonoidHom.transfer_sylow_eq_pow_aux /-
+#print MonoidHom.transferSylow_eq_pow_aux /-
 /-- Auxillary lemma in order to state `transfer_sylow_eq_pow`. -/
-theorem transfer_sylow_eq_pow_aux (g : G) (hg : g ∈ P) (k : ℕ) (g₀ : G)
-    (h : g₀⁻¹ * g ^ k * g₀ ∈ P) : g₀⁻¹ * g ^ k * g₀ = g ^ k :=
+theorem transferSylow_eq_pow_aux (g : G) (hg : g ∈ P) (k : ℕ) (g₀ : G) (h : g₀⁻¹ * g ^ k * g₀ ∈ P) :
+    g₀⁻¹ * g ^ k * g₀ = g ^ k :=
   by
   haveI : (P : Subgroup G).IsCommutative :=
     ⟨⟨fun a b => Subtype.ext (hP (le_normalizer b.2) a a.2)⟩⟩
   replace hg := (P : Subgroup G).pow_mem hg k
   obtain ⟨n, hn, h⟩ := P.conj_eq_normalizer_conj_of_mem (g ^ k) g₀ hg h
   exact h.trans (Commute.inv_mul_cancel (hP hn (g ^ k) hg).symm)
-#align monoid_hom.transfer_sylow_eq_pow_aux MonoidHom.transfer_sylow_eq_pow_aux
+#align monoid_hom.transfer_sylow_eq_pow_aux MonoidHom.transferSylow_eq_pow_aux
 -/
 
 variable [FiniteIndex (P : Subgroup G)]
@@ -270,7 +270,7 @@ variable [FiniteIndex (P : Subgroup G)]
 #print MonoidHom.transferSylow_eq_pow /-
 theorem transferSylow_eq_pow (g : G) (hg : g ∈ P) :
     transferSylow P hP g =
-      ⟨g ^ (P : Subgroup G).index, transfer_eq_pow_aux g (transfer_sylow_eq_pow_aux P hP g hg)⟩ :=
+      ⟨g ^ (P : Subgroup G).index, transfer_eq_pow_aux g (transferSylow_eq_pow_aux P hP g hg)⟩ :=
   by apply transfer_eq_pow
 #align monoid_hom.transfer_sylow_eq_pow MonoidHom.transferSylow_eq_pow
 -/

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -47,6 +47,7 @@ open scoped Pointwise
 
 variable (R S T : leftTransversals (H : Set G)) [FiniteIndex H]
 
+#print Subgroup.leftTransversals.diff /-
 /-- The difference of two left transversals -/
 @[to_additive "The difference of two left transversals"]
 noncomputable def diff : A :=
@@ -59,7 +60,9 @@ noncomputable def diff : A :=
           Quotient.exact' ((α.symm_apply_apply q).trans (β.symm_apply_apply q).symm)⟩
 #align subgroup.left_transversals.diff Subgroup.leftTransversals.diff
 #align add_subgroup.left_transversals.diff AddSubgroup.leftTransversals.diff
+-/
 
+#print Subgroup.leftTransversals.diff_mul_diff /-
 @[to_additive]
 theorem diff_mul_diff : diff ϕ R S * diff ϕ S T = diff ϕ R T :=
   prod_mul_distrib.symm.trans
@@ -69,19 +72,25 @@ theorem diff_mul_diff : diff ϕ R S * diff ϕ S T = diff ϕ R T :=
           (by simp_rw [Subtype.ext_iff, coe_mul, coe_mk, mul_assoc, mul_inv_cancel_left])))
 #align subgroup.left_transversals.diff_mul_diff Subgroup.leftTransversals.diff_mul_diff
 #align add_subgroup.left_transversals.diff_add_diff AddSubgroup.leftTransversals.diff_add_diff
+-/
 
+#print Subgroup.leftTransversals.diff_self /-
 @[to_additive]
 theorem diff_self : diff ϕ T T = 1 :=
   mul_right_eq_self.mp (diff_mul_diff ϕ T T T)
 #align subgroup.left_transversals.diff_self Subgroup.leftTransversals.diff_self
 #align add_subgroup.left_transversals.diff_self AddSubgroup.leftTransversals.diff_self
+-/
 
+#print Subgroup.leftTransversals.diff_inv /-
 @[to_additive]
 theorem diff_inv : (diff ϕ S T)⁻¹ = diff ϕ T S :=
   inv_eq_of_mul_eq_one_right <| (diff_mul_diff ϕ S T S).trans <| diff_self ϕ S
 #align subgroup.left_transversals.diff_inv Subgroup.leftTransversals.diff_inv
 #align add_subgroup.left_transversals.diff_neg AddSubgroup.leftTransversals.diff_neg
+-/
 
+#print Subgroup.leftTransversals.smul_diff_smul /-
 @[to_additive]
 theorem smul_diff_smul (g : G) : diff ϕ (g • S) (g • T) = diff ϕ S T :=
   let h := H.fintypeQuotientOfFiniteIndex
@@ -95,6 +104,7 @@ theorem smul_diff_smul (g : G) : diff ϕ (g • S) (g • T) = diff ϕ S T :=
     inv_smul_smul g q
 #align subgroup.left_transversals.smul_diff_smul Subgroup.leftTransversals.smul_diff_smul
 #align add_subgroup.left_transversals.vadd_diff_vadd AddSubgroup.leftTransversals.vadd_diff_vadd
+-/
 
 end LeftTransversals
 
@@ -104,6 +114,7 @@ namespace MonoidHom
 
 open MulAction Subgroup Subgroup.leftTransversals
 
+#print MonoidHom.transfer /-
 /-- Given `ϕ : H →* A` from `H : subgroup G` to a commutative group `A`,
 the transfer homomorphism is `transfer ϕ : G →* A`. -/
 @[to_additive
@@ -115,15 +126,19 @@ noncomputable def transfer [FiniteIndex H] : G →* A :=
     map_mul' := fun g h => by rw [mul_smul, ← diff_mul_diff, smul_diff_smul] }
 #align monoid_hom.transfer MonoidHom.transfer
 #align add_monoid_hom.transfer AddMonoidHom.transfer
+-/
 
 variable (T : leftTransversals (H : Set G))
 
+#print MonoidHom.transfer_def /-
 @[to_additive]
 theorem transfer_def [FiniteIndex H] (g : G) : transfer ϕ g = diff ϕ T (g • T) := by
   rw [transfer, ← diff_mul_diff, ← smul_diff_smul, mul_comm, diff_mul_diff] <;> rfl
 #align monoid_hom.transfer_def MonoidHom.transfer_def
 #align add_monoid_hom.transfer_def AddMonoidHom.transfer_def
+-/
 
+#print MonoidHom.transfer_eq_prod_quotient_orbitRel_zpowers_quot /-
 /-- Explicit computation of the transfer homomorphism. -/
 theorem transfer_eq_prod_quotient_orbitRel_zpowers_quot [FiniteIndex H] (g : G)
     [Fintype (Quotient (orbitRel (zpowers g) (G ⧸ H)))] :
@@ -147,7 +162,9 @@ theorem transfer_eq_prod_quotient_orbitRel_zpowers_quot [FiniteIndex H] (g : G)
   · simp only [if_neg hk, inv_mul_self]
     exact map_one ϕ
 #align monoid_hom.transfer_eq_prod_quotient_orbit_rel_zpowers_quot MonoidHom.transfer_eq_prod_quotient_orbitRel_zpowers_quot
+-/
 
+#print MonoidHom.transfer_eq_pow_aux /-
 /-- Auxillary lemma in order to state `transfer_eq_pow`. -/
 theorem transfer_eq_pow_aux (g : G)
     (key : ∀ (k : ℕ) (g₀ : G), g₀⁻¹ * g ^ k * g₀ ∈ H → g₀⁻¹ * g ^ k * g₀ = g ^ k) :
@@ -169,7 +186,9 @@ theorem transfer_eq_pow_aux (g : G)
   simpa only [minimal_period_eq_card, Finset.prod_pow_eq_pow_sum, Fintype.card_sigma,
     Fintype.card_congr (self_equiv_sigma_orbits (zpowers g) (G ⧸ H)), index_eq_card] using key
 #align monoid_hom.transfer_eq_pow_aux MonoidHom.transfer_eq_pow_aux
+-/
 
+#print MonoidHom.transfer_eq_pow /-
 theorem transfer_eq_pow [FiniteIndex H] (g : G)
     (key : ∀ (k : ℕ) (g₀ : G), g₀⁻¹ * g ^ k * g₀ ∈ H → g₀⁻¹ * g ^ k * g₀ = g ^ k) :
     transfer ϕ g = ϕ ⟨g ^ H.index, transfer_eq_pow_aux g key⟩ := by
@@ -186,14 +205,18 @@ theorem transfer_eq_pow [FiniteIndex H] (g : G)
   funext
   apply key
 #align monoid_hom.transfer_eq_pow MonoidHom.transfer_eq_pow
+-/
 
+#print MonoidHom.transfer_center_eq_pow /-
 theorem transfer_center_eq_pow [FiniteIndex (center G)] (g : G) :
     transfer (MonoidHom.id (center G)) g = ⟨g ^ (center G).index, (center G).pow_index_mem g⟩ :=
   transfer_eq_pow (id (center G)) g fun k _ hk => by rw [← mul_right_inj, hk, mul_inv_cancel_right]
 #align monoid_hom.transfer_center_eq_pow MonoidHom.transfer_center_eq_pow
+-/
 
 variable (G)
 
+#print MonoidHom.transferCenterPow /-
 /-- The transfer homomorphism `G →* center G`. -/
 noncomputable def transferCenterPow [FiniteIndex (center G)] : G →* center G
     where
@@ -201,21 +224,23 @@ noncomputable def transferCenterPow [FiniteIndex (center G)] : G →* center G
   map_one' := Subtype.ext (one_pow (center G).index)
   map_mul' a b := by simp_rw [← show ∀ g, (_ : center G) = _ from transfer_center_eq_pow, map_mul]
 #align monoid_hom.transfer_center_pow MonoidHom.transferCenterPow
+-/
 
 variable {G}
 
+#print MonoidHom.transferCenterPow_apply /-
 @[simp]
 theorem transferCenterPow_apply [FiniteIndex (center G)] (g : G) :
     ↑(transferCenterPow G g) = g ^ (center G).index :=
   rfl
 #align monoid_hom.transfer_center_pow_apply MonoidHom.transferCenterPow_apply
+-/
 
 section BurnsideTransfer
 
 variable {p : ℕ} (P : Sylow p G) (hP : (P : Subgroup G).normalizer ≤ (P : Subgroup G).centralizer)
 
-include hP
-
+#print MonoidHom.transferSylow /-
 /-- The homomorphism `G →* P` in Burnside's transfer theorem. -/
 noncomputable def transferSylow [FiniteIndex (P : Subgroup G)] : G →* (P : Subgroup G) :=
   @transfer G _ P P
@@ -223,9 +248,11 @@ noncomputable def transferSylow [FiniteIndex (P : Subgroup G)] : G →* (P : Sub
       ⟨⟨fun a b => Subtype.ext (hP (le_normalizer b.2) a a.2)⟩⟩)
     (MonoidHom.id P) _
 #align monoid_hom.transfer_sylow MonoidHom.transferSylow
+-/
 
 variable [Fact p.Prime] [Finite (Sylow p G)]
 
+#print MonoidHom.transfer_sylow_eq_pow_aux /-
 /-- Auxillary lemma in order to state `transfer_sylow_eq_pow`. -/
 theorem transfer_sylow_eq_pow_aux (g : G) (hg : g ∈ P) (k : ℕ) (g₀ : G)
     (h : g₀⁻¹ * g ^ k * g₀ ∈ P) : g₀⁻¹ * g ^ k * g₀ = g ^ k :=
@@ -236,20 +263,26 @@ theorem transfer_sylow_eq_pow_aux (g : G) (hg : g ∈ P) (k : ℕ) (g₀ : G)
   obtain ⟨n, hn, h⟩ := P.conj_eq_normalizer_conj_of_mem (g ^ k) g₀ hg h
   exact h.trans (Commute.inv_mul_cancel (hP hn (g ^ k) hg).symm)
 #align monoid_hom.transfer_sylow_eq_pow_aux MonoidHom.transfer_sylow_eq_pow_aux
+-/
 
 variable [FiniteIndex (P : Subgroup G)]
 
+#print MonoidHom.transferSylow_eq_pow /-
 theorem transferSylow_eq_pow (g : G) (hg : g ∈ P) :
     transferSylow P hP g =
       ⟨g ^ (P : Subgroup G).index, transfer_eq_pow_aux g (transfer_sylow_eq_pow_aux P hP g hg)⟩ :=
   by apply transfer_eq_pow
 #align monoid_hom.transfer_sylow_eq_pow MonoidHom.transferSylow_eq_pow
+-/
 
+#print MonoidHom.transferSylow_restrict_eq_pow /-
 theorem transferSylow_restrict_eq_pow :
     ⇑((transferSylow P hP).restrict (P : Subgroup G)) = (· ^ (P : Subgroup G).index) :=
   funext fun g => transferSylow_eq_pow P hP g g.2
 #align monoid_hom.transfer_sylow_restrict_eq_pow MonoidHom.transferSylow_restrict_eq_pow
+-/
 
+#print MonoidHom.ker_transferSylow_isComplement' /-
 /-- Burnside's normal p-complement theorem: If `N(P) ≤ C(P)`, then `P` has a normal complement. -/
 theorem ker_transferSylow_isComplement' : IsComplement' (transferSylow P hP).ker P :=
   by
@@ -265,12 +298,16 @@ theorem ker_transferSylow_isComplement' : IsComplement' (transferSylow P hP).ker
     ker_restrict, subgroup_of_map_subtype, Subgroup.map_bot, coe_top] at hf 
   exact is_complement'_of_disjoint_and_mul_eq_univ (disjoint_iff.2 hf.1) hf.2
 #align monoid_hom.ker_transfer_sylow_is_complement' MonoidHom.ker_transferSylow_isComplement'
+-/
 
+#print MonoidHom.not_dvd_card_ker_transferSylow /-
 theorem not_dvd_card_ker_transferSylow : ¬p ∣ Nat.card (transferSylow P hP).ker :=
   (ker_transferSylow_isComplement' P hP).index_eq_card ▸ not_dvd_index_sylow P <|
     mt index_eq_zero_of_relindex_eq_zero index_ne_zero_of_finite
 #align monoid_hom.not_dvd_card_ker_transfer_sylow MonoidHom.not_dvd_card_ker_transferSylow
+-/
 
+#print MonoidHom.ker_transferSylow_disjoint /-
 theorem ker_transferSylow_disjoint (Q : Subgroup G) (hQ : IsPGroup p Q) :
     Disjoint (transferSylow P hP).ker Q :=
   disjoint_iff.mpr <|
@@ -278,6 +315,7 @@ theorem ker_transferSylow_disjoint (Q : Subgroup G) (hQ : IsPGroup p Q) :
       (hQ.to_le inf_le_right).card_eq_or_dvd.resolve_right fun h =>
         not_dvd_card_ker_transferSylow P hP <| h.trans <| nat_card_dvd_of_le _ _ inf_le_left
 #align monoid_hom.ker_transfer_sylow_disjoint MonoidHom.ker_transferSylow_disjoint
+-/
 
 end BurnsideTransfer

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -140,7 +140,6 @@ theorem transfer_eq_prod_quotient_orbitRel_zpowers_quot [FiniteIndex H] (g : G)
     _ = _ := ((quotient_equiv_sigma_zmod H g).symm.prod_comp _).symm
     _ = _ := (Finset.prod_sigma _ _ _)
     _ = _ := Fintype.prod_congr _ _ fun q => _
-    
   simp only [quotient_equiv_sigma_zmod_symm_apply, transfer_transversal_apply',
     transfer_transversal_apply'']
   rw [Fintype.prod_eq_single (0 : ZMod (Function.minimalPeriod ((· • ·) g) q.out')) fun k hk => _]

bump to nightly-2023-06-07-03

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

831e78ce

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.transfer
-! leanprover-community/mathlib commit 56489b558d42c30f6aac5947cafc9a594f60813b
+! leanprover-community/mathlib commit 36938f775671ff28bea1c0310f1608e4afbb22e0
 ! 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.Sylow
 /-!
 # The Transfer Homomorphism
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we construct the transfer homomorphism.
 
 ## Main definitions

bump to nightly-2023-06-04-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

3fb4268b

Diff

@@ -131,19 +131,19 @@ theorem transfer_eq_prod_quotient_orbitRel_zpowers_quot [FiniteIndex H] (g : G)
             QuotientGroup.out'_conj_pow_minimalPeriod_mem H g q.out'⟩ :=
   by
   classical
-    letI := H.fintype_quotient_of_finite_index
-    calc
-      transfer ϕ g = ∏ q : G ⧸ H, _ := transfer_def ϕ (transfer_transversal H g) g
-      _ = _ := ((quotient_equiv_sigma_zmod H g).symm.prod_comp _).symm
-      _ = _ := (Finset.prod_sigma _ _ _)
-      _ = _ := Fintype.prod_congr _ _ fun q => _
-      
-    simp only [quotient_equiv_sigma_zmod_symm_apply, transfer_transversal_apply',
-      transfer_transversal_apply'']
-    rw [Fintype.prod_eq_single (0 : ZMod (Function.minimalPeriod ((· • ·) g) q.out')) fun k hk => _]
-    · simp only [if_pos, ZMod.cast_zero, zpow_zero, one_mul, mul_assoc]
-    · simp only [if_neg hk, inv_mul_self]
-      exact map_one ϕ
+  letI := H.fintype_quotient_of_finite_index
+  calc
+    transfer ϕ g = ∏ q : G ⧸ H, _ := transfer_def ϕ (transfer_transversal H g) g
+    _ = _ := ((quotient_equiv_sigma_zmod H g).symm.prod_comp _).symm
+    _ = _ := (Finset.prod_sigma _ _ _)
+    _ = _ := Fintype.prod_congr _ _ fun q => _
+    
+  simp only [quotient_equiv_sigma_zmod_symm_apply, transfer_transversal_apply',
+    transfer_transversal_apply'']
+  rw [Fintype.prod_eq_single (0 : ZMod (Function.minimalPeriod ((· • ·) g) q.out')) fun k hk => _]
+  · simp only [if_pos, ZMod.cast_zero, zpow_zero, one_mul, mul_assoc]
+  · simp only [if_neg hk, inv_mul_self]
+    exact map_one ϕ
 #align monoid_hom.transfer_eq_prod_quotient_orbit_rel_zpowers_quot MonoidHom.transfer_eq_prod_quotient_orbitRel_zpowers_quot
 
 /-- Auxillary lemma in order to state `transfer_eq_pow`. -/
@@ -155,35 +155,34 @@ theorem transfer_eq_pow_aux (g : G)
     exact H.one_mem
   letI := fintype_of_index_ne_zero hH
   classical
-    replace key : ∀ (k : ℕ) (g₀ : G), g₀⁻¹ * g ^ k * g₀ ∈ H → g ^ k ∈ H := fun k g₀ hk =>
-      (_root_.congr_arg (· ∈ H) (key k g₀ hk)).mp hk
-    replace key : ∀ q : G ⧸ H, g ^ Function.minimalPeriod ((· • ·) g) q ∈ H := fun q =>
-      key (Function.minimalPeriod ((· • ·) g) q) q.out'
-        (QuotientGroup.out'_conj_pow_minimalPeriod_mem H g q)
-    let f : Quotient (orbit_rel (zpowers g) (G ⧸ H)) → zpowers g := fun q =>
-      (⟨g, mem_zpowers g⟩ : zpowers g) ^ Function.minimalPeriod ((· • ·) g) q.out'
-    have hf : ∀ q, f q ∈ H.subgroup_of (zpowers g) := fun q => key q.out'
-    replace key :=
-      Subgroup.prod_mem (H.subgroup_of (zpowers g)) fun q (hq : q ∈ Finset.univ) => hf q
-    simpa only [minimal_period_eq_card, Finset.prod_pow_eq_pow_sum, Fintype.card_sigma,
-      Fintype.card_congr (self_equiv_sigma_orbits (zpowers g) (G ⧸ H)), index_eq_card] using key
+  replace key : ∀ (k : ℕ) (g₀ : G), g₀⁻¹ * g ^ k * g₀ ∈ H → g ^ k ∈ H := fun k g₀ hk =>
+    (_root_.congr_arg (· ∈ H) (key k g₀ hk)).mp hk
+  replace key : ∀ q : G ⧸ H, g ^ Function.minimalPeriod ((· • ·) g) q ∈ H := fun q =>
+    key (Function.minimalPeriod ((· • ·) g) q) q.out'
+      (QuotientGroup.out'_conj_pow_minimalPeriod_mem H g q)
+  let f : Quotient (orbit_rel (zpowers g) (G ⧸ H)) → zpowers g := fun q =>
+    (⟨g, mem_zpowers g⟩ : zpowers g) ^ Function.minimalPeriod ((· • ·) g) q.out'
+  have hf : ∀ q, f q ∈ H.subgroup_of (zpowers g) := fun q => key q.out'
+  replace key := Subgroup.prod_mem (H.subgroup_of (zpowers g)) fun q (hq : q ∈ Finset.univ) => hf q
+  simpa only [minimal_period_eq_card, Finset.prod_pow_eq_pow_sum, Fintype.card_sigma,
+    Fintype.card_congr (self_equiv_sigma_orbits (zpowers g) (G ⧸ H)), index_eq_card] using key
 #align monoid_hom.transfer_eq_pow_aux MonoidHom.transfer_eq_pow_aux
 
 theorem transfer_eq_pow [FiniteIndex H] (g : G)
     (key : ∀ (k : ℕ) (g₀ : G), g₀⁻¹ * g ^ k * g₀ ∈ H → g₀⁻¹ * g ^ k * g₀ = g ^ k) :
     transfer ϕ g = ϕ ⟨g ^ H.index, transfer_eq_pow_aux g key⟩ := by
   classical
-    letI := H.fintype_quotient_of_finite_index
-    change ∀ (k g₀) (hk : g₀⁻¹ * g ^ k * g₀ ∈ H), ↑(⟨g₀⁻¹ * g ^ k * g₀, hk⟩ : H) = g ^ k at key 
-    rw [transfer_eq_prod_quotient_orbit_rel_zpowers_quot, ← Finset.prod_to_list, List.prod_map_hom]
-    refine' congr_arg ϕ (Subtype.coe_injective _)
-    rw [H.coe_mk, ← (zpowers g).coe_mk g (mem_zpowers g), ← (zpowers g).coe_pow, (zpowers g).coe_mk,
-      index_eq_card, Fintype.card_congr (self_equiv_sigma_orbits (zpowers g) (G ⧸ H)),
-      Fintype.card_sigma, ← Finset.prod_pow_eq_pow_sum, ← Finset.prod_to_list]
-    simp only [coe_list_prod, List.map_map, ← minimal_period_eq_card]
-    congr 2
-    funext
-    apply key
+  letI := H.fintype_quotient_of_finite_index
+  change ∀ (k g₀) (hk : g₀⁻¹ * g ^ k * g₀ ∈ H), ↑(⟨g₀⁻¹ * g ^ k * g₀, hk⟩ : H) = g ^ k at key 
+  rw [transfer_eq_prod_quotient_orbit_rel_zpowers_quot, ← Finset.prod_to_list, List.prod_map_hom]
+  refine' congr_arg ϕ (Subtype.coe_injective _)
+  rw [H.coe_mk, ← (zpowers g).coe_mk g (mem_zpowers g), ← (zpowers g).coe_pow, (zpowers g).coe_mk,
+    index_eq_card, Fintype.card_congr (self_equiv_sigma_orbits (zpowers g) (G ⧸ H)),
+    Fintype.card_sigma, ← Finset.prod_pow_eq_pow_sum, ← Finset.prod_to_list]
+  simp only [coe_list_prod, List.map_map, ← minimal_period_eq_card]
+  congr 2
+  funext
+  apply key
 #align monoid_hom.transfer_eq_pow MonoidHom.transfer_eq_pow
 
 theorem transfer_center_eq_pow [FiniteIndex (center G)] (g : G) :

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -174,7 +174,7 @@ theorem transfer_eq_pow [FiniteIndex H] (g : G)
     transfer ϕ g = ϕ ⟨g ^ H.index, transfer_eq_pow_aux g key⟩ := by
   classical
     letI := H.fintype_quotient_of_finite_index
-    change ∀ (k g₀) (hk : g₀⁻¹ * g ^ k * g₀ ∈ H), ↑(⟨g₀⁻¹ * g ^ k * g₀, hk⟩ : H) = g ^ k at key
+    change ∀ (k g₀) (hk : g₀⁻¹ * g ^ k * g₀ ∈ H), ↑(⟨g₀⁻¹ * g ^ k * g₀, hk⟩ : H) = g ^ k at key 
     rw [transfer_eq_prod_quotient_orbit_rel_zpowers_quot, ← Finset.prod_to_list, List.prod_map_hom]
     refine' congr_arg ϕ (Subtype.coe_injective _)
     rw [H.coe_mk, ← (zpowers g).coe_mk g (mem_zpowers g), ← (zpowers g).coe_pow, (zpowers g).coe_mk,
@@ -257,11 +257,11 @@ theorem ker_transferSylow_isComplement' : IsComplement' (transferSylow P hP).ker
       (P.2.powEquiv'
           (not_dvd_index_sylow P
             (mt index_eq_zero_of_relindex_eq_zero index_ne_zero_of_finite))).Bijective
-  rw [Function.Bijective, ← range_top_iff_surjective, restrict_range] at hf
+  rw [Function.Bijective, ← range_top_iff_surjective, restrict_range] at hf 
   have := range_top_iff_surjective.mp (top_le_iff.mp (hf.2.ge.trans (map_le_range _ P)))
   rw [← (comap_injective this).eq_iff, comap_top, comap_map_eq, sup_comm, SetLike.ext'_iff,
     normal_mul, ← ker_eq_bot_iff, ← (map_injective (P : Subgroup G).subtype_injective).eq_iff,
-    ker_restrict, subgroup_of_map_subtype, Subgroup.map_bot, coe_top] at hf
+    ker_restrict, subgroup_of_map_subtype, Subgroup.map_bot, coe_top] at hf 
   exact is_complement'_of_disjoint_and_mul_eq_univ (disjoint_iff.2 hf.1) hf.2
 #align monoid_hom.ker_transfer_sylow_is_complement' MonoidHom.ker_transferSylow_isComplement'

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -30,7 +30,7 @@ In this file we construct the transfer homomorphism.
 -/
 
 
-open BigOperators
+open scoped BigOperators
 
 variable {G : Type _} [Group G] {H : Subgroup G} {A : Type _} [CommGroup A] (ϕ : H →* A)
 
@@ -40,7 +40,7 @@ namespace LeftTransversals
 
 open Finset MulAction
 
-open Pointwise
+open scoped Pointwise
 
 variable (R S T : leftTransversals (H : Set G)) [FiniteIndex H]

bump to nightly-2023-03-15-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a313d8bba1bad05faba71a4a4e9742ab5bd9efd

4e269297

Diff

@@ -177,10 +177,9 @@ theorem transfer_eq_pow [FiniteIndex H] (g : G)
     change ∀ (k g₀) (hk : g₀⁻¹ * g ^ k * g₀ ∈ H), ↑(⟨g₀⁻¹ * g ^ k * g₀, hk⟩ : H) = g ^ k at key
     rw [transfer_eq_prod_quotient_orbit_rel_zpowers_quot, ← Finset.prod_to_list, List.prod_map_hom]
     refine' congr_arg ϕ (Subtype.coe_injective _)
-    rw [H.coe_mk, ← (zpowers g).coe_mk g (mem_zpowers g), ← (zpowers g).val_pow_eq_pow_val,
-      (zpowers g).coe_mk, index_eq_card,
-      Fintype.card_congr (self_equiv_sigma_orbits (zpowers g) (G ⧸ H)), Fintype.card_sigma, ←
-      Finset.prod_pow_eq_pow_sum, ← Finset.prod_to_list]
+    rw [H.coe_mk, ← (zpowers g).coe_mk g (mem_zpowers g), ← (zpowers g).coe_pow, (zpowers g).coe_mk,
+      index_eq_card, Fintype.card_congr (self_equiv_sigma_orbits (zpowers g) (G ⧸ H)),
+      Fintype.card_sigma, ← Finset.prod_pow_eq_pow_sum, ← Finset.prod_to_list]
     simp only [coe_list_prod, List.map_map, ← minimal_period_eq_card]
     congr 2
     funext

bump to nightly-2023-03-01-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

20cadee0

Diff

@@ -135,7 +135,7 @@ theorem transfer_eq_prod_quotient_orbitRel_zpowers_quot [FiniteIndex H] (g : G)
     calc
       transfer ϕ g = ∏ q : G ⧸ H, _ := transfer_def ϕ (transfer_transversal H g) g
       _ = _ := ((quotient_equiv_sigma_zmod H g).symm.prod_comp _).symm
-      _ = _ := Finset.prod_sigma _ _ _
+      _ = _ := (Finset.prod_sigma _ _ _)
       _ = _ := Fintype.prod_congr _ _ fun q => _
       
     simp only [quotient_equiv_sigma_zmod_symm_apply, transfer_transversal_apply',

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

chore: refactor to avoid importing Ring for Group topics (#11913)

This is a far from a complete success at the PR title, but it makes a fair bit of progress, and then guards this with appropriate assert_not_exists Ring statements.

It also breaks apart the Mathlib.GroupTheory.Subsemigroup.[Center|Centralizer] files, to pull the Set.center and Set.centralizer declarations into their own files not depending on Subsemigroup.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

8e052acc

Diff

@@ -5,6 +5,7 @@ Authors: Thomas Browning
 -/
 import Mathlib.GroupTheory.Complement
 import Mathlib.GroupTheory.Sylow
+import Mathlib.GroupTheory.Subgroup.Center
 
 #align_import group_theory.transfer from "leanprover-community/mathlib"@"4be589053caf347b899a494da75410deb55fb3ef"

chore: classify porting notes about additional necessary beta reduction (#12130)

This subsumes some of the notes in #10752 and #10971. I'm on the fence as to whether replacing the dsimp only by beta_reduce is useful; this is easy to revert if needed.

7eeaaffb

Diff

@@ -100,7 +100,9 @@ the transfer homomorphism is `transfer ϕ : G →+ A`."]
 noncomputable def transfer [FiniteIndex H] : G →* A :=
   let T : leftTransversals (H : Set G) := Inhabited.default
   { toFun := fun g => diff ϕ T (g • T)
-    map_one' := by simp only; rw [one_smul, diff_self] -- Porting note: added `simp only`
+    -- Porting note(#12129): additional beta reduction needed
+    map_one' := by beta_reduce; rw [one_smul, diff_self]
+    -- Porting note: added `simp only` (not just beta reduction)
     map_mul' := fun g h => by simp only; rw [mul_smul, ← diff_mul_diff, smul_diff_smul] }
 #align monoid_hom.transfer MonoidHom.transfer
 #align add_monoid_hom.transfer AddMonoidHom.transfer

chore: superfluous parentheses part 2 (#12131)

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

d48d30ac

Diff

@@ -126,7 +126,7 @@ theorem transfer_eq_prod_quotient_orbitRel_zpowers_quot [FiniteIndex H] (g : G)
     calc
       transfer ϕ g = ∏ q : G ⧸ H, _ := transfer_def ϕ (transferTransversal H g) g
       _ = _ := ((quotientEquivSigmaZMod H g).symm.prod_comp _).symm
-      _ = _ := (Finset.prod_sigma _ _ _)
+      _ = _ := Finset.prod_sigma _ _ _
       _ = _ := by
         refine' Fintype.prod_congr _ _ (fun q => _)
         simp only [quotientEquivSigmaZMod_symm_apply, transferTransversal_apply',

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

@@ -100,7 +100,7 @@ the transfer homomorphism is `transfer ϕ : G →+ A`."]
 noncomputable def transfer [FiniteIndex H] : G →* A :=
   let T : leftTransversals (H : Set G) := Inhabited.default
   { toFun := fun g => diff ϕ T (g • T)
-    map_one' := by simp only; rw [one_smul, diff_self] -- porting note: added `simp only`
+    map_one' := by simp only; rw [one_smul, diff_self] -- Porting note: added `simp only`
     map_mul' := fun g h => by simp only; rw [mul_smul, ← diff_mul_diff, smul_diff_smul] }
 #align monoid_hom.transfer MonoidHom.transfer
 #align add_monoid_hom.transfer AddMonoidHom.transfer
@@ -168,9 +168,9 @@ theorem transfer_eq_pow [FiniteIndex H] (g : G)
     letI := H.fintypeQuotientOfFiniteIndex
     change ∀ (k g₀) (hk : g₀⁻¹ * g ^ k * g₀ ∈ H), ↑(⟨g₀⁻¹ * g ^ k * g₀, hk⟩ : H) = g ^ k at key
     rw [transfer_eq_prod_quotient_orbitRel_zpowers_quot, ← Finset.prod_to_list]
-    refine' (List.prod_map_hom _ _ _).trans _ -- porting note: this used to be in the `rw`
+    refine' (List.prod_map_hom _ _ _).trans _ -- Porting note: this used to be in the `rw`
     refine' congrArg ϕ (Subtype.coe_injective _)
-    simp only -- porting note: added `simp only`
+    simp only -- Porting note: added `simp only`
     rw [H.coe_mk, ← (zpowers g).coe_mk g (mem_zpowers g), ← (zpowers g).coe_pow,
       index_eq_card, Fintype.card_congr (selfEquivSigmaOrbits (zpowers g) (G ⧸ H)),
       Fintype.card_sigma, ← Finset.prod_pow_eq_pow_sum, ← Finset.prod_to_list]
@@ -234,7 +234,7 @@ theorem transferSylow_eq_pow (g : G) (hg : g ∈ P) :
       ⟨g ^ (P : Subgroup G).index, transfer_eq_pow_aux g (transferSylow_eq_pow_aux P hP g hg)⟩ :=
   @transfer_eq_pow G _ P P (@Subgroup.IsCommutative.commGroup G _ P
     ⟨⟨fun a b => Subtype.ext (hP (le_normalizer b.2) a a.2)⟩⟩) _ _ g
-      (transferSylow_eq_pow_aux P hP g hg) -- porting note: apply used to do this automatically
+      (transferSylow_eq_pow_aux P hP g hg) -- Porting note: apply used to do this automatically
 #align monoid_hom.transfer_sylow_eq_pow MonoidHom.transferSylow_eq_pow
 
 theorem transferSylow_restrict_eq_pow : ⇑((transferSylow P hP).restrict (P : Subgroup G)) =

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

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

38bce757

Diff

@@ -157,7 +157,7 @@ theorem transfer_eq_pow_aux (g : G)
     have hf : ∀ q, f q ∈ H.subgroupOf (zpowers g) := fun q => key q.out'
     replace key :=
       Subgroup.prod_mem (H.subgroupOf (zpowers g)) fun q (_ : q ∈ Finset.univ) => hf q
-    simpa only [minimalPeriod_eq_card, Finset.prod_pow_eq_pow_sum, Fintype.card_sigma,
+    simpa only [f, minimalPeriod_eq_card, Finset.prod_pow_eq_pow_sum, Fintype.card_sigma,
       Fintype.card_congr (selfEquivSigmaOrbits (zpowers g) (G ⧸ H)), index_eq_card] using key
 #align monoid_hom.transfer_eq_pow_aux MonoidHom.transfer_eq_pow_aux

chore(*): drop $/<| before fun (#9361)

Subset of #9319

3694e27d

Diff

@@ -79,7 +79,7 @@ theorem diff_inv : (diff ϕ S T)⁻¹ = diff ϕ T S :=
 @[to_additive]
 theorem smul_diff_smul (g : G) : diff ϕ (g • S) (g • T) = diff ϕ S T :=
   let _ := H.fintypeQuotientOfFiniteIndex
-  Fintype.prod_equiv (MulAction.toPerm g).symm _ _ $ fun _ ↦ by
+  Fintype.prod_equiv (MulAction.toPerm g).symm _ _ fun _ ↦ by
     simp only [smul_apply_eq_smul_apply_inv_smul, smul_eq_mul, mul_inv_rev, mul_assoc,
       inv_mul_cancel_left, toPerm_symm_apply]
 #align subgroup.left_transversals.smul_diff_smul Subgroup.leftTransversals.smul_diff_smul

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

@@ -79,14 +79,9 @@ theorem diff_inv : (diff ϕ S T)⁻¹ = diff ϕ T S :=
 @[to_additive]
 theorem smul_diff_smul (g : G) : diff ϕ (g • S) (g • T) = diff ϕ S T :=
   let _ := H.fintypeQuotientOfFiniteIndex
-  prod_bij' (fun q _ => g⁻¹ • q) (fun _ _ => mem_univ _)
-    (fun _ _ =>
-      congr_arg ϕ
-        (by
-          simp_rw [smul_apply_eq_smul_apply_inv_smul, smul_eq_mul, mul_inv_rev, mul_assoc,
-            inv_mul_cancel_left]))
-    (fun q _ => g • q) (fun _ _ => mem_univ _) (fun q _ => smul_inv_smul g q) fun q _ =>
-    inv_smul_smul g q
+  Fintype.prod_equiv (MulAction.toPerm g).symm _ _ $ fun _ ↦ by
+    simp only [smul_apply_eq_smul_apply_inv_smul, smul_eq_mul, mul_inv_rev, mul_assoc,
+      inv_mul_cancel_left, toPerm_symm_apply]
 #align subgroup.left_transversals.smul_diff_smul Subgroup.leftTransversals.smul_diff_smul
 #align add_subgroup.left_transversals.vadd_diff_vadd AddSubgroup.leftTransversals.vadd_diff_vadd

chore: Replace (· op ·) a by (a op ·) (#8843)

I used the regex $\(· (.) ·$ (.)\), replacing with ($2 $1 ·).

d14658b4

Diff

@@ -124,7 +124,7 @@ theorem transfer_eq_prod_quotient_orbitRel_zpowers_quot [FiniteIndex H] (g : G)
     transfer ϕ g =
       ∏ q : Quotient (orbitRel (zpowers g) (G ⧸ H)),
         ϕ
-          ⟨q.out'.out'⁻¹ * g ^ Function.minimalPeriod ((· • ·) g) q.out' * q.out'.out',
+          ⟨q.out'.out'⁻¹ * g ^ Function.minimalPeriod (g • ·) q.out' * q.out'.out',
             QuotientGroup.out'_conj_pow_minimalPeriod_mem H g q.out'⟩ := by
   classical
     letI := H.fintypeQuotientOfFiniteIndex
@@ -136,7 +136,7 @@ theorem transfer_eq_prod_quotient_orbitRel_zpowers_quot [FiniteIndex H] (g : G)
         refine' Fintype.prod_congr _ _ (fun q => _)
         simp only [quotientEquivSigmaZMod_symm_apply, transferTransversal_apply',
           transferTransversal_apply'']
-        rw [Fintype.prod_eq_single (0 : ZMod (Function.minimalPeriod ((· • ·) g) q.out')) _]
+        rw [Fintype.prod_eq_single (0 : ZMod (Function.minimalPeriod (g • ·) q.out')) _]
         · simp only [if_pos, ZMod.cast_zero, zpow_zero, one_mul, mul_assoc]
         · intro k hk
           simp only [if_neg hk, inv_mul_self]
@@ -154,11 +154,11 @@ theorem transfer_eq_pow_aux (g : G)
   classical
     replace key : ∀ (k : ℕ) (g₀ : G), g₀⁻¹ * g ^ k * g₀ ∈ H → g ^ k ∈ H := fun k g₀ hk =>
       (_root_.congr_arg (· ∈ H) (key k g₀ hk)).mp hk
-    replace key : ∀ q : G ⧸ H, g ^ Function.minimalPeriod ((· • ·) g) q ∈ H := fun q =>
-      key (Function.minimalPeriod ((· • ·) g) q) q.out'
+    replace key : ∀ q : G ⧸ H, g ^ Function.minimalPeriod (g • ·) q ∈ H := fun q =>
+      key (Function.minimalPeriod (g • ·) q) q.out'
         (QuotientGroup.out'_conj_pow_minimalPeriod_mem H g q)
     let f : Quotient (orbitRel (zpowers g) (G ⧸ H)) → zpowers g := fun q =>
-      (⟨g, mem_zpowers g⟩ : zpowers g) ^ Function.minimalPeriod ((· • ·) g) q.out'
+      (⟨g, mem_zpowers g⟩ : zpowers g) ^ Function.minimalPeriod (g • ·) q.out'
     have hf : ∀ q, f q ∈ H.subgroupOf (zpowers g) := fun q => key q.out'
     replace key :=
       Subgroup.prod_mem (H.subgroupOf (zpowers g)) fun q (_ : q ∈ Finset.univ) => hf q

doc: Mark named theorems (#8749)

a3708498

Diff

@@ -247,7 +247,8 @@ theorem transferSylow_restrict_eq_pow : ⇑((transferSylow P hP).restrict (P : S
   funext fun g => transferSylow_eq_pow P hP g g.2
 #align monoid_hom.transfer_sylow_restrict_eq_pow MonoidHom.transferSylow_restrict_eq_pow
 
-/-- Burnside's normal p-complement theorem: If `N(P) ≤ C(P)`, then `P` has a normal complement. -/
+/-- **Burnside's normal p-complement theorem**: If `N(P) ≤ C(P)`, then `P` has a normal
+complement. -/
 theorem ker_transferSylow_isComplement' : IsComplement' (transferSylow P hP).ker P := by
   have hf : Function.Bijective ((transferSylow P hP).restrict (P : Subgroup G)) :=
     (transferSylow_restrict_eq_pow P hP).symm ▸

chore: space after ← (#8178)

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

5fb9beab

Diff

@@ -187,7 +187,7 @@ theorem transfer_eq_pow [FiniteIndex H] (g : G)
 
 theorem transfer_center_eq_pow [FiniteIndex (center G)] (g : G) :
     transfer (MonoidHom.id (center G)) g = ⟨g ^ (center G).index, (center G).pow_index_mem g⟩ :=
-  transfer_eq_pow (id (center G)) g fun k _ hk => by rw [← mul_right_inj, ←hk.comm,
+  transfer_eq_pow (id (center G)) g fun k _ hk => by rw [← mul_right_inj, ← hk.comm,
     mul_inv_cancel_right]
 #align monoid_hom.transfer_center_eq_pow MonoidHom.transfer_center_eq_pow

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

@@ -187,7 +187,8 @@ theorem transfer_eq_pow [FiniteIndex H] (g : G)
 
 theorem transfer_center_eq_pow [FiniteIndex (center G)] (g : G) :
     transfer (MonoidHom.id (center G)) g = ⟨g ^ (center G).index, (center G).pow_index_mem g⟩ :=
-  transfer_eq_pow (id (center G)) g fun k _ hk => by rw [← mul_right_inj, hk, mul_inv_cancel_right]
+  transfer_eq_pow (id (center G)) g fun k _ hk => by rw [← mul_right_inj, ←hk.comm,
+    mul_inv_cancel_right]
 #align monoid_hom.transfer_center_eq_pow MonoidHom.transfer_center_eq_pow
 
 variable (G)

chore: exactly 4 spaces in theorems (#7328)

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

d3263b23

Diff

@@ -242,7 +242,7 @@ theorem transferSylow_eq_pow (g : G) (hg : g ∈ P) :
 #align monoid_hom.transfer_sylow_eq_pow MonoidHom.transferSylow_eq_pow
 
 theorem transferSylow_restrict_eq_pow : ⇑((transferSylow P hP).restrict (P : Subgroup G)) =
-  (fun x : P => x ^ (P : Subgroup G).index) :=
+    (fun x : P => x ^ (P : Subgroup G).index) :=
   funext fun g => transferSylow_eq_pow P hP g g.2
 #align monoid_hom.transfer_sylow_restrict_eq_pow MonoidHom.transferSylow_restrict_eq_pow

chore: remove unused simps (#6632)

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

916c75c1

Diff

@@ -60,7 +60,7 @@ theorem diff_mul_diff : diff ϕ R S * diff ϕ S T = diff ϕ R T :=
     (prod_congr rfl fun q _ =>
       (ϕ.map_mul _ _).symm.trans
         (congr_arg ϕ
-          (by simp_rw [Subtype.ext_iff, coe_mul, coe_mk, mul_assoc, mul_inv_cancel_left])))
+          (by simp_rw [Subtype.ext_iff, coe_mul, mul_assoc, mul_inv_cancel_left])))
 #align subgroup.left_transversals.diff_mul_diff Subgroup.leftTransversals.diff_mul_diff
 #align add_subgroup.left_transversals.diff_add_diff AddSubgroup.leftTransversals.diff_add_diff
 
@@ -83,7 +83,7 @@ theorem smul_diff_smul (g : G) : diff ϕ (g • S) (g • T) = diff ϕ S T :=
     (fun _ _ =>
       congr_arg ϕ
         (by
-          simp_rw [coe_mk, smul_apply_eq_smul_apply_inv_smul, smul_eq_mul, mul_inv_rev, mul_assoc,
+          simp_rw [smul_apply_eq_smul_apply_inv_smul, smul_eq_mul, mul_inv_rev, mul_assoc,
             inv_mul_cancel_left]))
     (fun q _ => g • q) (fun _ _ => mem_univ _) (fun q _ => smul_inv_smul g q) fun q _ =>
     inv_smul_smul g q

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

@@ -29,7 +29,7 @@ In this file we construct the transfer homomorphism.
 
 open scoped BigOperators
 
-variable {G : Type _} [Group G] {H : Subgroup G} {A : Type _} [CommGroup A] (ϕ : H →* A)
+variable {G : Type*} [Group G] {H : Subgroup G} {A : Type*} [CommGroup A] (ϕ : H →* A)
 
 namespace Subgroup

chore(GroupTheory): forward-port leanprover-community/mathlib#18965 (#6147)

13e7c2f0

Diff

@@ -6,7 +6,7 @@ Authors: Thomas Browning
 import Mathlib.GroupTheory.Complement
 import Mathlib.GroupTheory.Sylow
 
-#align_import group_theory.transfer from "leanprover-community/mathlib"@"56489b558d42c30f6aac5947cafc9a594f60813b"
+#align_import group_theory.transfer from "leanprover-community/mathlib"@"4be589053caf347b899a494da75410deb55fb3ef"
 
 /-!
 # The Transfer Homomorphism
@@ -209,7 +209,7 @@ theorem transferCenterPow_apply [FiniteIndex (center G)] (g : G) :
 
 section BurnsideTransfer
 
-variable {p : ℕ} (P : Sylow p G) (hP : (P : Subgroup G).normalizer ≤ (P : Subgroup G).centralizer)
+variable {p : ℕ} (P : Sylow p G) (hP : (P : Subgroup G).normalizer ≤ centralizer (P : Set G))
 
 /-- The homomorphism `G →* P` in Burnside's transfer theorem. -/
 noncomputable def transferSylow [FiniteIndex (P : Subgroup G)] : G →* (P : Subgroup G) :=

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) 2022 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.transfer
-! leanprover-community/mathlib commit 56489b558d42c30f6aac5947cafc9a594f60813b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.GroupTheory.Complement
 import Mathlib.GroupTheory.Sylow
 
+#align_import group_theory.transfer from "leanprover-community/mathlib"@"56489b558d42c30f6aac5947cafc9a594f60813b"
+
 /-!
 # The Transfer Homomorphism

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

@@ -144,8 +144,7 @@ theorem transfer_eq_prod_quotient_orbitRel_zpowers_quot [FiniteIndex H] (g : G)
         · intro k hk
           simp only [if_neg hk, inv_mul_self]
           exact map_one ϕ
-#align monoid_hom.transfer_eq_prod_quotient_orbit_rel_zpowers_quot
-  MonoidHom.transfer_eq_prod_quotient_orbitRel_zpowers_quot
+#align monoid_hom.transfer_eq_prod_quotient_orbit_rel_zpowers_quot MonoidHom.transfer_eq_prod_quotient_orbitRel_zpowers_quot
 
 /-- Auxiliary lemma in order to state `transfer_eq_pow`. -/
 theorem transfer_eq_pow_aux (g : G)

chore: tidy various files (#5104)

62d90431

Diff

@@ -20,12 +20,12 @@ In this file we construct the transfer homomorphism.
 
 - `diff ϕ S T` : The difference of two left transversals `S` and `T` under the homomorphism `ϕ`.
 - `transfer ϕ` : The transfer homomorphism induced by `ϕ`.
-- `transfer_center_pow`: The transfer homomorphism `G →* center G`.
+- `transferCenterPow`: The transfer homomorphism `G →* center G`.
 
 ## Main results
-- `transfer_center_pow_apply`:
+- `transferCenterPow_apply`:
   The transfer homomorphism `G →* center G` is given by `g ↦ g ^ (center G).index`.
-- `ker_transfer_sylow_is_complement'`: Burnside's transfer (or normal `p`-complement) theorem:
+- `ker_transferSylow_isComplement'`: Burnside's transfer (or normal `p`-complement) theorem:
   If `hP : N(P) ≤ C(P)`, then `(transfer P hP).ker` is a normal `p`-complement.
 -/
 
@@ -225,24 +225,24 @@ noncomputable def transferSylow [FiniteIndex (P : Subgroup G)] : G →* (P : Sub
 
 variable [Fact p.Prime] [Finite (Sylow p G)]
 
-/-- Auxiliary lemma in order to state `transfer_sylow_eq_pow`. -/
-theorem transfer_sylow_eq_pow_aux (g : G) (hg : g ∈ P) (k : ℕ) (g₀ : G)
+/-- Auxiliary lemma in order to state `transferSylow_eq_pow`. -/
+theorem transferSylow_eq_pow_aux (g : G) (hg : g ∈ P) (k : ℕ) (g₀ : G)
     (h : g₀⁻¹ * g ^ k * g₀ ∈ P) : g₀⁻¹ * g ^ k * g₀ = g ^ k := by
   haveI : (P : Subgroup G).IsCommutative :=
     ⟨⟨fun a b => Subtype.ext (hP (le_normalizer b.2) a a.2)⟩⟩
   replace hg := (P : Subgroup G).pow_mem hg k
   obtain ⟨n, hn, h⟩ := P.conj_eq_normalizer_conj_of_mem (g ^ k) g₀ hg h
   exact h.trans (Commute.inv_mul_cancel (hP hn (g ^ k) hg).symm)
-#align monoid_hom.transfer_sylow_eq_pow_aux MonoidHom.transfer_sylow_eq_pow_aux
+#align monoid_hom.transfer_sylow_eq_pow_aux MonoidHom.transferSylow_eq_pow_aux
 
 variable [FiniteIndex (P : Subgroup G)]
 
 theorem transferSylow_eq_pow (g : G) (hg : g ∈ P) :
     transferSylow P hP g =
-      ⟨g ^ (P : Subgroup G).index, transfer_eq_pow_aux g (transfer_sylow_eq_pow_aux P hP g hg)⟩ :=
+      ⟨g ^ (P : Subgroup G).index, transfer_eq_pow_aux g (transferSylow_eq_pow_aux P hP g hg)⟩ :=
   @transfer_eq_pow G _ P P (@Subgroup.IsCommutative.commGroup G _ P
     ⟨⟨fun a b => Subtype.ext (hP (le_normalizer b.2) a a.2)⟩⟩) _ _ g
-      (transfer_sylow_eq_pow_aux P hP g hg) -- porting note: apply used to do this automatically
+      (transferSylow_eq_pow_aux P hP g hg) -- porting note: apply used to do this automatically
 #align monoid_hom.transfer_sylow_eq_pow MonoidHom.transferSylow_eq_pow
 
 theorem transferSylow_restrict_eq_pow : ⇑((transferSylow P hP).restrict (P : Subgroup G)) =

chore: fix many typos (#4983)

These are all doc fixes

54b72114

Diff

@@ -147,7 +147,7 @@ theorem transfer_eq_prod_quotient_orbitRel_zpowers_quot [FiniteIndex H] (g : G)
 #align monoid_hom.transfer_eq_prod_quotient_orbit_rel_zpowers_quot
   MonoidHom.transfer_eq_prod_quotient_orbitRel_zpowers_quot
 
-/-- Auxillary lemma in order to state `transfer_eq_pow`. -/
+/-- Auxiliary lemma in order to state `transfer_eq_pow`. -/
 theorem transfer_eq_pow_aux (g : G)
     (key : ∀ (k : ℕ) (g₀ : G), g₀⁻¹ * g ^ k * g₀ ∈ H → g₀⁻¹ * g ^ k * g₀ = g ^ k) :
     g ^ H.index ∈ H := by
@@ -225,7 +225,7 @@ noncomputable def transferSylow [FiniteIndex (P : Subgroup G)] : G →* (P : Sub
 
 variable [Fact p.Prime] [Finite (Sylow p G)]
 
-/-- Auxillary lemma in order to state `transfer_sylow_eq_pow`. -/
+/-- Auxiliary lemma in order to state `transfer_sylow_eq_pow`. -/
 theorem transfer_sylow_eq_pow_aux (g : G) (hg : g ∈ P) (k : ℕ) (g₀ : G)
     (h : g₀⁻¹ * g ^ k * g₀ ∈ P) : g₀⁻¹ * g ^ k * g₀ = g ^ k := by
   haveI : (P : Subgroup G).IsCommutative :=

chore: tidy various files (#4854)

5238ba14

Diff

@@ -133,11 +133,11 @@ theorem transfer_eq_prod_quotient_orbitRel_zpowers_quot [FiniteIndex H] (g : G)
     letI := H.fintypeQuotientOfFiniteIndex
     calc
       transfer ϕ g = ∏ q : G ⧸ H, _ := transfer_def ϕ (transferTransversal H g) g
-      _ = _ := ((quotientEquivSigmaZmod H g).symm.prod_comp _).symm
+      _ = _ := ((quotientEquivSigmaZMod H g).symm.prod_comp _).symm
       _ = _ := (Finset.prod_sigma _ _ _)
       _ = _ := by
         refine' Fintype.prod_congr _ _ (fun q => _)
-        simp only [quotientEquivSigmaZmod_symm_apply, transferTransversal_apply',
+        simp only [quotientEquivSigmaZMod_symm_apply, transferTransversal_apply',
           transferTransversal_apply'']
         rw [Fintype.prod_eq_single (0 : ZMod (Function.minimalPeriod ((· • ·) g) q.out')) _]
         · simp only [if_pos, ZMod.cast_zero, zpow_zero, one_mul, mul_assoc]
@@ -263,7 +263,7 @@ theorem ker_transferSylow_isComplement' : IsComplement' (transferSylow P hP).ker
   rw [← (comap_injective this).eq_iff, comap_top, comap_map_eq, sup_comm, SetLike.ext'_iff,
     normal_mul, ← ker_eq_bot_iff, ← (map_injective (P : Subgroup G).subtype_injective).eq_iff,
     ker_restrict, subgroupOf_map_subtype, Subgroup.map_bot, coe_top] at hf
-  exact IsComplement'_of_disjoint_and_mul_eq_univ (disjoint_iff.2 hf.1) hf.2
+  exact isComplement'_of_disjoint_and_mul_eq_univ (disjoint_iff.2 hf.1) hf.2
 #align monoid_hom.ker_transfer_sylow_is_complement' MonoidHom.ker_transferSylow_isComplement'
 
 theorem not_dvd_card_ker_transferSylow : ¬p ∣ Nat.card (transferSylow P hP).ker :=