Theorems · Theorem · group theory
Sylow.card_dvd_index
- #72 of the 100 theorems: Sylow’s Theorem
- 1000+ list: Sylow theorems
∀ {p : ℕ} {G : Type u_1} [inst : Group G] [Fact (Nat.Prime p)] [Finite (Sylow p G)] (P : Sylow p G),
Nat.card (Sylow p G) ∣ (↑P).index- Defined in
- Mathlib.GroupTheory.Sylow
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
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
- 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
- Subgroup.indexstatement · cited by 150
- Dvd.dvd.transproof · cited by 148
- Sylowstatement and proof · cited by 103
- Sylow.toSubgroupstatement · cited by 86
- dvd_rflproof · cited by 80
- Subgroup.le_normalizerproof · cited by 19
- Subgroup.index_dvd_of_leproof · cited by 8
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