Theorems · Theorem · group theory
alternatingGroup.two_sylow_eq_kleinFour_of_card_eq_four
∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : Fintype α],
Nat.card α = 4 → ∀ (S : Sylow 2 ↥(alternatingGroup α)), ↑S = alternatingGroup.kleinFour α- Cited by
- 4 results in Mathlib
- Foundations
- Depth 125 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.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Fintypestatement and proof · cited by 7,736
- Set.ofPredproof · cited by 6,101
- Subgroupstatement and proof · cited by 3,593
- Equiv.Permstatement and proof · cited by 1,375
- Nat.cardstatement and proof · cited by 844
- Subgroup.closureproof · cited by 196
- Sylowstatement and proof · cited by 103
- alternatingGroupstatement and proof · cited by 96
- Equiv.Perm.cycleTypeproof · cited by 87
- Sylow.toSubgroupstatement and proof · cited by 86
- Set.singleton_unionproof · cited by 22
Cited by4
Results whose statement or proof uses this declaration.
- alternatingGroup.coe_kleinFour_of_card_eq_fourproof · cited by 3
- alternatingGroup.kleinFour_card_of_card_eq_fourproof · cited by 3
- alternatingGroup.characteristic_kleinFourproof · cited by 1
- alternatingGroup.subsingleton_two_sylowproof · cited by 1