Theorems · Theorem · group theory
Equiv.Perm.isCycle_of_prime_order
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] {σ : Equiv.Perm α},
Nat.Prime (orderOf σ) → σ.support.card < 2 * orderOf σ → σ.IsCycle- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Type
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- Multisetproof · cited by 2,627
- Finset.cardstatement and proof · cited by 2,327
- Nat.Primestatement and proof · cited by 2,059
- Equiv.Permstatement and proof · cited by 1,375
- Multiset.sumproof · cited by 388
- Multiset.cardproof · cited by 375
- nsmul_eq_mulproof · cited by 369
- orderOfstatement and proof · cited by 324
- Equiv.Perm.supportstatement and proof · cited by 230
- Equiv.Perm.IsCyclestatement · cited by 108
- Multiset.replicateproof · cited by 88
Cited by1
Results whose statement or proof uses this declaration.
- Equiv.Perm.isCycle_of_prime_order'proof · cited by 1