Theorems · Theorem · group theory
Equiv.Perm.IsCycle.support_pow_eq_iff
∀ {α : Type u_2} {f : Equiv.Perm α} [inst : DecidableEq α] [inst_1 : Fintype α],
f.IsCycle → ∀ {n : ℕ}, (f ^ n).support = f.support ↔ ¬orderOf f ∣ n- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 76 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.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Finsetstatement and proof · 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
- Equiv.injectiveproof · cited by 464
- orderOfstatement · cited by 324
- Equiv.Perm.supportstatement and proof · cited by 230
- Equiv.Perm.IsCyclestatement and proof · cited by 108
- Commute.eqproof · cited by 91
- Equiv.Perm.extproof · cited by 75
- Equiv.Perm.mem_supportproof · cited by 51
Cited by4
Results whose statement or proof uses this declaration.
- Equiv.Perm.nodup_toListproof · cited by 5
- Equiv.Perm.IsCycle.pow_eq_one_iffproof · cited by 3
- Equiv.Perm.IsCycle.pow_iffproof · cited by 1
- Equiv.Perm.IsCycle.support_pow_of_pos_of_lt_orderOfproof · cited by 1