Theorems · Theorem · group theory
Equiv.Perm.isConj_iff_cycleType_eq
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] {σ τ : Equiv.Perm α},
IsConj σ τ ↔ σ.cycleType = τ.cycleType- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Type
- Cited by
- 4 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.
Cites8
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
- Multisetstatement and proof · cited by 2,627
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.Perm.cycleTypestatement and proof · cited by 87
- IsConjstatement and proof · cited by 43
- isConj_iffproof · cited by 16
- Equiv.Perm.cycleType_conjproof · cited by 2
- Equiv.Perm.isConj_of_cycleType_eqproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- alternatingGroup.isThreeCycle_isConjproof · cited by 1
- alternatingGroup.kleinFour_eq_commutatorproof · cited by 0
- Equiv.Perm.partition_eq_of_isConjproof · cited by 0
- alternatingGroup.isConj_swap_mul_swap_of_cycleType_twoproof · cited by 0