Theorems · Theorem · group theory
Sylow.card_coprime_index
∀ {G : Type u} [inst : Group G] [Finite G] {p : ℕ} [hp : Fact (Nat.Prime p)] (P : Sylow p G),
(Nat.card ↥↑P).Coprime (↑P).indexSylow subgroups are Hall subgroups.
- Defined in
- Mathlib.GroupTheory.Sylow
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- Finitestatement and proof · cited by 3,029
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- Nat.cardstatement and proof · cited by 844
- Fact.outproof · cited by 328
- Subgroup.indexstatement and proof · cited by 150
- Sylowstatement and proof · cited by 103
- Sylow.toSubgroupstatement and proof · cited by 86
- Sylow.isPGroup'proof · cited by 19
- Sylow.not_dvd_indexproof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- Sylow.le_center_or_le_commutatorproof · cited by 1
- Sylow.commutator_eq_bot_or_commutator_eq_selfproof · cited by 1