Theorems · Theorem · group theory
Subgroup.commutator_inf_eq_focalSubgroup
- 1000+ list: Focal subgroup theorem
∀ {G : Type u_1} [inst : Group G] {p : ℕ} [Fact (Nat.Prime p)] (P : Sylow p G) [(↑P).FiniteIndex],
commutator G ⊓ ↑P = (↑P).focalSubgroupThe Focal Subgroup Theorem
For a Sylow p-subgroup P of a finite group G, P ∩ G' = P*,
where P* is the focal subgroup of P.
- Defined in
- Mathlib.GroupTheory.Focal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
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- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- Factstatement and proof · cited by 2,726
- le_antisymmproof · cited by 2,068
- Nat.Primestatement and proof · cited by 2,059
- le_transproof · cited by 985
- Eq.leproof · cited by 605
- Subgroup.FiniteIndexstatement and proof · cited by 113
- le_infproof · cited by 107
- Sylowstatement and proof · cited by 103
- Sylow.toSubgroupstatement and proof · cited by 86
- commutatorstatement · cited by 56
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