Theorems · Theorem · group theory
Equiv.Perm.IsCycle.forall_commute_iff
∀ {α : Type u_2} [inst : DecidableEq α] [inst_1 : Fintype α] (g z : Equiv.Perm α),
(∀ c ∈ g.cycleFactorsFinset, Commute z c) ↔
∀ c ∈ g.cycleFactorsFinset,
∃ (hc : ∀ (x : α), z x ∈ c.support ↔ x ∈ c.support), Equiv.Perm.ofSubtype (z.subtypePerm hc) ∈ Subgroup.zpowers c- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Factors
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintype
Around this declaration
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Finsetstatement · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- MonoidHomstatement · cited by 3,629
- Subgroupstatement · cited by 3,593
- Equiv.Permstatement and proof · cited by 1,375
- Commutestatement · cited by 639
- Equiv.Perm.supportstatement · cited by 230
- Subgroup.zpowersstatement · cited by 204
- Equiv.Perm.cycleFactorsFinsetstatement and proof · cited by 96
- Equiv.Perm.ofSubtypestatement · cited by 41
- Equiv.Perm.subtypePermstatement · cited by 35
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