Theorems · Theorem · group theory
Sylow.dvd_card_of_dvd_card
∀ {G : Type u} [inst : Group G] [Finite G] {p : ℕ} [Fact (Nat.Prime p)] (P : Sylow p G),
p ∣ Nat.card G → p ∣ Nat.card ↥↑P- Defined in
- Mathlib.GroupTheory.Sylow
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- pow_oneproof · cited by 894
- Nat.cardstatement and proof · cited by 844
- Sylowstatement and proof · cited by 103
- Sylow.toSubgroupstatement and proof · cited by 86
- Sylow.pow_dvd_card_of_pow_dvd_cardproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Sylow.ne_bot_of_dvd_cardproof · cited by 1