Theorems · Theorem · group theory
Equiv.Perm.support_pow_coprime
∀ {α : Type u} [inst : DecidableEq α] [inst_1 : Fintype α] {σ : Equiv.Perm α} {n : ℕ},
n.Coprime (orderOf σ) → (σ ^ n).support = σ.support- Defined in
- Mathlib.GroupTheory.Perm.Finite
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintype
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.
- Finsetstatement · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- le_antisymmproof · cited by 2,068
- Equiv.Permstatement and proof · cited by 1,375
- le_transproof · cited by 985
- orderOfstatement and proof · cited by 324
- Equiv.Perm.supportstatement and proof · cited by 230
- ge_of_eqproof · cited by 67
- Equiv.Perm.support_pow_leproof · cited by 5
- exists_pow_eq_self_of_coprimeproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Equiv.Perm.IsThreeCycle.isThreeCycle_sqproof · cited by 2
- Equiv.Perm.closure_cycle_coprime_swapproof · cited by 1