Theorems · Theorem · group theory
nat_card_alternatingGroup
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] [Nontrivial α],
Nat.card ↥(alternatingGroup α) = (Nat.card α).factorial / 2- Cited by
- 2 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEqNontrivial
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 · cited by 3,593
- Nontrivialstatement and proof · cited by 2,416
- Fintype.cardproof · cited by 1,386
- Equiv.Permstatement · cited by 1,375
- Nat.cardstatement · cited by 844
- Nat.factorialstatement and proof · cited by 616
- Nat.card_eq_fintype_cardproof · cited by 200
- alternatingGroupstatement · cited by 96
- card_alternatingGroupproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- alternatingGroup.card_of_card_eq_fourproof · cited by 2
- alternatingGroup.isCyclic_of_card_le_threeproof · cited by 1