Theorems · Theorem · group theory
Equiv.Perm.IsThreeCycle.orderOf
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] {g : Equiv.Perm α}, g.IsThreeCycle → orderOf g = 3- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Type
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 101 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.
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
- Multisetproof · cited by 2,627
- Equiv.Permstatement and proof · cited by 1,375
- orderOfstatement · cited by 324
- Equiv.Perm.IsThreeCyclestatement and proof · cited by 34
- normalize_eqproof · cited by 26
- Multiset.lcmproof · cited by 20
- Equiv.Perm.lcm_cycleTypeproof · cited by 7
- Equiv.Perm.IsThreeCycle.cycleTypeproof · cited by 5
- Multiset.lcm_singletonproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- Equiv.Perm.IsThreeCycle.support_eq_iff_mem_supportproof · cited by 3
- Equiv.Perm.IsThreeCycle.isThreeCycle_sqproof · cited by 2
- Equiv.Perm.alternatingGroup_le_of_isPreprimitive_of_isThreeCycle_memproof · cited by 2
- Equiv.Perm.IsThreeCycle.eq_swap_mul_swap_iff_mem_supportproof · cited by 1