Theorems · Theorem · group theory
Equiv.Perm.alternatingGroup_le_of_index_le_two
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] {G : Subgroup (Equiv.Perm α)},
G.index ≤ 2 → alternatingGroup α ≤ GA subgroup of the permutation group of index ≤ 2 contains the alternating group.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 100 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.
- Fintypestatement and proof · cited by 7,736
- Subgroupstatement and proof · cited by 3,593
- le_reflproof · cited by 2,061
- Equiv.Permstatement and proof · cited by 1,375
- LE.le.antisymmproof · cited by 507
- le_topproof · cited by 411
- Subgroup.indexstatement and proof · cited by 150
- alternatingGroupstatement and proof · cited by 96
- LE.le.eq_or_lt'proof · cited by 27
- Subgroup.index_eq_oneproof · cited by 9
- Subgroup.index_ne_zero_of_finiteproof · cited by 5
- Equiv.Perm.eq_alternatingGroup_of_index_eq_twoproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Equiv.Perm.alternatingGroup_le_of_isPreprimitive_of_isThreeCycle_memproof · cited by 2
- IsMultiplyPretransitive.alternatingGroup_leproof · cited by 1