Theorems · Definition · group theory
Equiv.Perm.cycleFactorsFinset
{α : Type u_2} → [DecidableEq α] → [Fintype α] → Equiv.Perm α → Finset (Equiv.Perm α)Factors a permutation f into a Finset of disjoint cyclic permutations that multiply to f.
- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Factors
- Cited by
- 96 results in Mathlib
- Foundations
- Depth 90 from the axioms, rests on 2,088 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Equiv.Permstatement and proof · cited by 1,375
- Multiset.ofListproof · cited by 290
- Equiv.Perm.IsCycleproof · cited by 108
- Equiv.Perm.Disjointproof · cited by 81
- Trunc.liftproof · cited by 5
- Equiv.Perm.truncCycleFactorsproof · cited by 3
Cited by110
Results whose statement or proof uses this declaration.
- Equiv.Perm.cycleTypeproof · cited by 87
- Equiv.Perm.mem_cycleFactorsFinset_iffstatement and proof · cited by 17
- Equiv.Perm.OnCycleFactors.range_toPermHom'statement and proof · cited by 16
- Equiv.Perm.Disjoint.cycleType_mulproof · cited by 14
- Equiv.Perm.OnCycleFactors.toPermHomstatement and proof · cited by 12
- Equiv.Perm.cycleFactorsFinset_pairwise_disjointstatement · cited by 10
- Equiv.Perm.OnCycleFactors.kerParamstatement · cited by 10
- Equiv.Perm.Basis.ofPermHomFunstatement and proof · cited by 9
- Equiv.Perm.cycleFactorsFinset_mem_commutestatement · cited by 7
- Equiv.Perm.cycleOf_mem_cycleFactorsFinset_iffstatement · cited by 7
- Equiv.Perm.cycleType_defstatement · cited by 7
- Equiv.Perm.mem_cycleFactorsFinset_support_lestatement and proof · cited by 7