Theorems · Theorem · group theory
Equiv.Perm.IsThreeCycle.mem_commutator_alternatingGroup
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α],
5 ≤ Nat.card α → ∀ {g : ↥(alternatingGroup α)}, (↑g).IsThreeCycle → g ∈ commutator ↥(alternatingGroup α)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 105 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
- Subgroupstatement and proof · cited by 3,593
- Equiv.Permstatement and proof · cited by 1,375
- Nat.cardstatement and proof · cited by 844
- alternatingGroupstatement and proof · cited by 96
- commutatorstatement · cited by 56
- Subgroup.subset_closureproof · cited by 53
- Equiv.Perm.IsThreeCyclestatement and proof · cited by 34
- commutator_eq_closureproof · cited by 7
- Equiv.Perm.IsThreeCycle.mem_commutatorSet_alternatingGroupproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- commutator_alternatingGroup_eq_topproof · cited by 3