Theorems · Definition · group theory
Equiv.Perm.IsCycle.zpowersEquivSupport
{α : Type u_2} →
[inst : DecidableEq α] → [inst_1 : Fintype α] → {σ : Equiv.Perm α} → σ.IsCycle → ↥(Subgroup.zpowers σ) ≃ ↥σ.supportThe subgroup generated by a cycle is in bijection with its support
- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 61 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Finsetstatement · cited by 13,712
- Equivstatement · cited by 8,337
- SetLike.coeproof · cited by 8,199
- Fintypestatement and proof · cited by 7,736
- Set.Elemproof · cited by 7,166
- Subgroupstatement · cited by 3,593
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.Perm.supportstatement · cited by 230
- Subgroup.zpowersstatement and proof · cited by 204
- Equiv.Perm.IsCyclestatement and proof · cited by 108
- Equiv.ofBijectiveproof · cited by 70
Cited by5
Results whose statement or proof uses this declaration.
- Equiv.Perm.IsCycle.orderOfproof · cited by 14
- Equiv.Perm.IsCycle.isConjproof · cited by 2
- Equiv.Perm.IsCycle.zpowersEquivSupport_applystatement · cited by 1
- Equiv.Perm.IsCycle.zpowersEquivSupport_symm_applystatement and proof · cited by 1
- Equiv.Perm.IsCycle.zpowersEquivSupport.congr_simpstatement and proof · cited by 0