Theorems · Theorem · group theory
Equiv.Perm.commute_ofSubtype_noncommPiCoprod
∀ {α : Type u_2} [inst : DecidableEq α] [inst_1 : Fintype α] (f : Equiv.Perm α)
(u : Equiv.Perm ↑(Function.fixedPoints ⇑f)) (v : (c : ↥f.cycleFactorsFinset) → ↥(Subgroup.zpowers ↑c)),
Commute (Equiv.Perm.ofSubtype u) ((Subgroup.noncommPiCoprod ⋯) v)- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Factors
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Finsetstatement · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- MonoidHomstatement · cited by 3,629
- Subgroupstatement · cited by 3,593
- Equiv.Permstatement and proof · cited by 1,375
- Commutestatement · cited by 639
- Subgroup.zpowersstatement and proof · cited by 204
- Equiv.Perm.cycleFactorsFinsetstatement and proof · cited by 96
- Function.fixedPointsstatement and proof · cited by 90
Cited by6
Results whose statement or proof uses this declaration.
- Equiv.Perm.OnCycleFactors.kerParamproof · cited by 10
- Equiv.Perm.OnCycleFactors.kerParam_range_eqproof · cited by 3
- Equiv.Perm.OnCycleFactors.sign_kerParam_apply_applyproof · cited by 2
- Equiv.Perm.OnCycleFactors.kerParam_applyproof · cited by 1
- Equiv.Perm.OnCycleFactors.kerParam_injectiveproof · cited by 1
- Equiv.Perm.OnCycleFactors.cycleType_kerParam_apply_applyproof · cited by 0