Theorems · Theorem · group theory
alternatingGroup.coe_two_sylow_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 = {1} ∪ {g | (↑g).cycleType = {2, 2}}- Cited by
- 2 results in Mathlib
- Foundations
- Depth 124 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.
Cites44
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
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- Fintypestatement and proof · cited by 7,736
- Set.ofPredstatement and proof · cited by 6,101
- Subgroupstatement · cited by 3,593
- Finset.univproof · cited by 3,473
- LE.le.transproof · cited by 3,151
- Multisetstatement · cited by 2,627
- Finset.prodproof · cited by 2,356
- Finset.cardproof · cited by 2,327
- Equiv.Permstatement and proof · cited by 1,375
Cited by2
Results whose statement or proof uses this declaration.
- alternatingGroup.two_sylow_eq_kleinFour_of_card_eq_fourproof · cited by 4
- alternatingGroup.coe_kleinFour_of_card_eq_fourproof · cited by 3