Theorems · Theorem · group theory
Equiv.Perm.IsCycle.pow_iff
∀ {β : Type u_3} [Finite β] {f : Equiv.Perm β}, f.IsCycle → ∀ {n : ℕ}, (f ^ n).IsCycle ↔ n.Coprime (orderOf f)- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Basic
- Cited by
- 1 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.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- Fintypeproof · cited by 7,736
- Finitestatement and proof · cited by 3,029
- Finset.cardproof · cited by 2,327
- LT.lt.ne'proof · cited by 1,417
- Equiv.Permstatement and proof · cited by 1,375
- one_powproof · cited by 521
- orderOfstatement and proof · cited by 324
- nonempty_fintypeproof · cited by 261
- Equiv.Perm.supportproof · cited by 230
- pow_mulproof · cited by 210
- Equiv.Perm.IsCyclestatement and proof · cited by 108
Cited by1
Results whose statement or proof uses this declaration.
- Equiv.Perm.IsCycle.isCycle_pow_pos_of_lt_prime_orderproof · cited by 0