Theorems · Theorem · group theory
alternatingGroup.subsingleton_two_sylow
∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : Fintype α],
Nat.card α = 4 → Subsingleton (Sylow 2 ↥(alternatingGroup α))- Cited by
- 1 results in Mathlib
- Foundations
- Depth 126 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
- Equiv.Permstatement and proof · cited by 1,375
- Nat.cardstatement and proof · cited by 844
- Sylowstatement and proof · cited by 103
- alternatingGroupstatement and proof · cited by 96
- alternatingGroup.kleinFourproof · cited by 11
- Sylow.ext_iffproof · cited by 5
- alternatingGroup.two_sylow_eq_kleinFour_of_card_eq_fourproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- alternatingGroup.characteristic_kleinFourproof · cited by 1