Theorems · Theorem · group theory
Sylow.card_eq_multiplicity
∀ {G : Type u} [inst : Group G] [Finite G] {p : ℕ} [hp : Fact (Nat.Prime p)] (P : Sylow p G),
Nat.card ↥↑P = p ^ (Nat.card G).factorization pThe cardinality of a Sylow subgroup is p ^ n
where n is the multiplicity of p in the group order.
- Defined in
- Mathlib.GroupTheory.Sylow
- Cited by
- 2 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.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Groupstatement and proof · cited by 6,238
- Finsuppstatement · cited by 5,255
- 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
- LT.lt.ne'proof · cited by 1,417
- Nat.cardstatement and proof · cited by 844
- Fact.outproof · cited by 328
- Nat.factorizationstatement and proof · cited by 215
- Sylowstatement and proof · cited by 103
Cited by2
Results whose statement or proof uses this declaration.
- alternatingGroup.card_two_sylow_of_card_eq_fourproof · cited by 2
- IsZGroup.exponent_eq_cardproof · cited by 0