Theorems · Theorem · group theory
Equiv.Perm.IsCycle.pow_eq_one_iff
∀ {β : Type u_3} [Finite β] {f : Equiv.Perm β}, f.IsCycle → ∀ {n : ℕ}, f ^ n = 1 ↔ ∃ x, f x ≠ x ∧ (f ^ n) x = x- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Finite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Finsetproof · cited by 13,712
- Fintypeproof · cited by 7,736
- Finitestatement and proof · cited by 3,029
- Equiv.Permstatement and proof · cited by 1,375
- one_powproof · cited by 521
- orderOfproof · cited by 324
- nonempty_fintypeproof · cited by 261
- Equiv.Perm.supportproof · cited by 230
- pow_mulproof · cited by 210
- Equiv.Perm.SameCycleproof · cited by 116
- Equiv.Perm.IsCyclestatement and proof · cited by 108
Cited by3
Results whose statement or proof uses this declaration.
- Equiv.Perm.IsCycle.pow_eq_one_iff'proof · cited by 2
- Equiv.Perm.cycle_zpow_mem_support_iffproof · cited by 1
- Equiv.Perm.IsCycle.pow_eq_pow_iffproof · cited by 0