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Mathlib.GroupTheory.Perm.ConjAct

Some lemmas pertaining to the action of ConjAct (Perm α) on Perm α #

We prove some lemmas related to the action of ConjAct (Perm α) on Perm α:

Let α be a decidable fintype.

theorem Equiv.Perm.mem_conj_support {α : Type u_1} [DecidableEq α] [Fintype α] (k : ConjAct (Perm α)) (g : Perm α) (a : α) :

a : α belongs to the support of k • g iff k⁻¹ * a belongs to the support of g

@[simp]

A permutation c is a cycle of g iff k • c is a cycle of k • g