Theorems · Definition · group theory
Equiv.Perm.IsThreeCycle
{α : Type u_1} → [Fintype α] → [DecidableEq α] → Equiv.Perm α → PropA three-cycle is a cycle of length 3.
- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Type
- Cited by
- 34 results in Mathlib
- Foundations
- Depth 92 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.
Cites3
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
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.Perm.cycleTypeproof · cited by 87
Cited by34
Results whose statement or proof uses this declaration.
- Equiv.Perm.IsThreeCycle.card_supportstatement and proof · cited by 6
- Equiv.Perm.IsThreeCycle.cycleTypestatement and proof · cited by 5
- Equiv.Perm.IsThreeCycle.mem_alternatingGroupstatement and proof · cited by 5
- Equiv.Perm.IsThreeCycle.orderOfstatement and proof · cited by 4
- commutator_alternatingGroup_eq_topproof · cited by 3
- Equiv.Perm.closure_three_cycles_eq_alternatingstatement and proof · cited by 3
- Equiv.Perm.IsThreeCycle.isCyclestatement and proof · cited by 3
- card_support_eq_three_iffstatement and proof · cited by 3
- Equiv.Perm.IsThreeCycle.support_eq_iff_mem_supportstatement and proof · cited by 3
- Equiv.Perm.exists_mem_stabilizer_isThreeCyclestatement and proof · cited by 2
- Equiv.Perm.closure_cycleType_eq_two_two_eq_alternatingGroupproof · cited by 2
- Equiv.Perm.IsThreeCycle.congr_simpstatement and proof · cited by 2