Theorems · Theorem · group theory
Equiv.Perm.cycleType_of_pow_prime_eq_one
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] {σ : Equiv.Perm α} {p : ℕ} [Fact (Nat.Prime p)],
σ ^ p = 1 → σ.cycleType = Multiset.replicate σ.cycleType.card p- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Type
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEqFact
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Factstatement and proof · cited by 2,726
- Multisetstatement · cited by 2,627
- Nat.Primestatement and proof · cited by 2,059
- Equiv.Permstatement and proof · cited by 1,375
- Multiset.cardstatement · cited by 375
- Multiset.replicatestatement · cited by 88
- Equiv.Perm.cycleTypestatement · cited by 87
- Multiset.eq_replicateproof · cited by 9
- Equiv.Perm.pow_prime_eq_one_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Equiv.Perm.sign_of_pow_two_eq_oneproof · cited by 1