Theorems · Theorem · group theory
Equiv.Perm.IsCycle.isCycle_pow_pos_of_lt_prime_order
∀ {β : Type u_3} [Finite β] {f : Equiv.Perm β},
f.IsCycle → Nat.Prime (orderOf f) → ∀ (n : ℕ), 0 < n → n < orderOf f → (f ^ n).IsCycle- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Finite
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypeproof · cited by 7,736
- Finitestatement and proof · cited by 3,029
- Nat.Primestatement and proof · cited by 2,059
- Equiv.Permstatement and proof · cited by 1,375
- orderOfstatement and proof · cited by 324
- nonempty_fintypeproof · cited by 261
- Equiv.Perm.IsCyclestatement and proof · cited by 108
- Nat.Prime.coprime_iff_not_dvdproof · cited by 38
- Equiv.Perm.IsCycle.pow_iffproof · cited by 1
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