Theorems · Theorem · group theory
Sylow.normalizer_le_centralizer_or_le_commutator
∀ {G : Type u_1} [inst : Group G] {p : ℕ} [Fact (Nat.Prime p)] [Finite G] (P : Sylow p G) [IsCyclic ↥↑P],
Subgroup.normalizer ↑P ≤ Subgroup.centralizer ↑P ∨ ↑P ≤ commutator GA cyclic Sylow subgroup is either central in its normalizer or contained in the commutator subgroup.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites42
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- MulEquiv.symmproof · cited by 482
- le_topproof · cited by 411
Cited by1
Results whose statement or proof uses this declaration.
- Sylow.not_dvd_card_commutator_or_not_dvd_index_commutatorproof · cited by 1