Theorems · Theorem · group theory
alternatingGroup.card_of_card_eq_four
∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : Fintype α], Nat.card α = 4 → Nat.card ↥(alternatingGroup α) = 12- Cited by
- 2 results in Mathlib
- Foundations
- Depth 102 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.
Cites9
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
- Nontrivialproof · cited by 2,416
- Equiv.Permstatement · cited by 1,375
- Nat.cardstatement and proof · cited by 844
- Nat.factorialproof · cited by 616
- alternatingGroupstatement · cited by 96
- Finite.one_lt_card_iff_nontrivialproof · cited by 11
- nat_card_alternatingGroupproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- alternatingGroup.card_two_sylow_of_card_eq_fourproof · cited by 2
- alternatingGroup.kleinFour_eq_commutatorproof · cited by 0