Theorems · Theorem · group theory
Equiv.Perm.IsThreeCycle.sign
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] {σ : Equiv.Perm α}, σ.IsThreeCycle → Equiv.Perm.sign σ = 1- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Type
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 102 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Fintypestatement and proof · cited by 7,736
- MonoidHomstatement · cited by 3,629
- Unitsstatement and proof · cited by 2,804
- Multisetproof · cited by 2,627
- Equiv.Permstatement and proof · cited by 1,375
- Multiset.sumproof · cited by 388
- Multiset.cardproof · cited by 375
- Equiv.Perm.signstatement · cited by 138
- Equiv.Perm.IsThreeCyclestatement and proof · cited by 34
- Equiv.Perm.sign_of_cycleTypeproof · cited by 7
- Equiv.Perm.IsThreeCycle.cycleTypeproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Equiv.Perm.IsThreeCycle.mem_alternatingGroupproof · cited by 5