Theorems · Theorem · group theory
Equiv.Perm.pow_prime_eq_one_iff
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] {σ : Equiv.Perm α} {p : ℕ} [hp : Fact (Nat.Prime p)],
σ ^ p = 1 ↔ ∀ c ∈ σ.cycleType, c = p- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Type
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 101 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.
Cites13
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
- dvd_reflproof · cited by 97
- Equiv.Perm.cycleTypestatement and proof · cited by 87
- Fact.elimproof · cited by 25
- orderOf_dvd_iff_pow_eq_oneproof · cited by 22
- Nat.Prime.eq_one_or_self_of_dvdproof · cited by 11
- Equiv.Perm.lcm_cycleTypeproof · cited by 7
- Multiset.lcm_dvdproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Equiv.Perm.count_le_one_of_centralizer_le_alternatingproof · cited by 1
- Equiv.Perm.cycleType_of_pow_prime_eq_oneproof · cited by 1