Theorems · Theorem · group theory
alternatingGroup.commutator_perm_eq
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α],
5 ≤ Nat.card α → commutator (Equiv.Perm α) = alternatingGroup αThe commutator subgroup of the permutation group is the alternating group
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 110 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.
Cites11
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
- le_antisymmproof · cited by 2,068
- Equiv.Permstatement and proof · cited by 1,375
- Nat.cardstatement and proof · cited by 844
- le_topproof · cited by 411
- alternatingGroupstatement · cited by 96
- commutatorstatement and proof · cited by 56
- Subgroup.commutator_monoproof · cited by 11
- commutator_alternatingGroup_eq_selfproof · cited by 1
- alternatingGroup.commutator_perm_leproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Equiv.Perm.alternatingGroup_le_of_normalproof · cited by 0