Theorems · Definition · group theory
alternatingGroup
(α : Type u_1) → [Fintype α] → [DecidableEq α] → Subgroup (Equiv.Perm α)
The alternating group on a finite type, realized as a subgroup of Equiv.Perm.
For $A_n$, use alternatingGroup (Fin n).
- Cited by
- 96 results in Mathlib
- Foundations
- Depth 78 from the axioms, rests on 1,922 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 · cited by 3,593
- Equiv.Permstatement · cited by 1,375
- MonoidHom.kerproof · cited by 212
- Equiv.Perm.signproof · cited by 138
Cited by101
Results whose statement or proof uses this declaration.
- alternatingGroup.kleinFourstatement and proof · cited by 11
- alternatingGroup.ofSubtypestatement and proof · cited by 9
- Equiv.Perm.mem_alternatingGroupstatement · cited by 7
- Equiv.Perm.IsThreeCycle.mem_alternatingGroupstatement · cited by 5
- alternatingGroup.isMultiplyPretransitivestatement and proof · cited by 4
- alternatingGroup.two_sylow_eq_kleinFour_of_card_eq_fourstatement and proof · cited by 4
- two_mul_nat_card_alternatingGroupstatement and proof · cited by 3
- alternatingGroup.coe_kleinFour_of_card_eq_fourstatement and proof · cited by 3
- Equiv.Perm.closure_three_cycles_eq_alternatingstatement and proof · cited by 3
- alternatingGroup.isSimpleGroupstatement and proof · cited by 3
- alternatingGroup.kleinFour_card_of_card_eq_fourstatement and proof · cited by 3
- AlternatingGroup.map_subtype_of_cycleTypestatement and proof · cited by 3