Theorems · Theorem · group theory
Sylow.pow_dvd_card_of_pow_dvd_card
∀ {G : Type u} [inst : Group G] [Finite G] {p n : ℕ} [hp : Fact (Nat.Prime p)] (P : Sylow p G),
p ^ n ∣ Nat.card G → p ^ n ∣ Nat.card ↥↑P- 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.
Cites12
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
- Sylowstatement and proof · cited by 103
- Sylow.toSubgroupstatement and proof · cited by 86
- Sylow.not_dvd_indexproof · cited by 9
- Subgroup.index_mul_cardproof · cited by 7
- Nat.Prime.coprime_pow_of_not_dvdproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Sylow.card_eq_multiplicityproof · cited by 2
- Sylow.dvd_card_of_dvd_cardproof · cited by 1