Theorems · Theorem · group theory
alternatingGroup.isSimpleGroup
∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : Fintype α], 5 ≤ Nat.card α → IsSimpleGroup ↥(alternatingGroup α)When α has at least 5 elements, then alternatingGroup α is a simple group.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintype
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
- Subgroupstatement and proof · cited by 3,593
- Equiv.Permstatement and proof · cited by 1,375
- Nat.cardstatement and proof · cited by 844
- Subgroup.Normalproof · cited by 334
- alternatingGroupstatement and proof · cited by 96
- IsSimpleGroupstatement · cited by 26
- alternatingGroup.normal_subgroup_eq_bot_or_eq_topproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Equiv.Perm.IsThreeCycle.alternating_normalClosureproof · cited by 0
- alternatingGroup.normalClosure_finRotate_fiveproof · cited by 0
- alternatingGroup.normalClosure_swap_mul_swap_fiveproof · cited by 0