Theorems · Theorem · group theory
Sylow.normal_of_normalizerCondition
∀ {G : Type u} [inst : Group G],
NormalizerCondition G → ∀ {p : ℕ} [Fact (Nat.Prime p)] [Finite (Sylow p G)] (P : Sylow p G), (↑P).Normal- Defined in
- Mathlib.GroupTheory.Sylow
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 118 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.
- SetLike.coeproof · cited by 8,199
- 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
- Subgroup.Normalstatement · cited by 334
- Subgroup.normalizerproof · cited by 108
- Sylowstatement and proof · cited by 103
- Sylow.toSubgroupstatement and proof · cited by 86
- Subgroup.normalizer_eq_top_iffproof · cited by 10
- NormalizerConditionstatement and proof · cited by 8
- normalizerCondition_iff_only_full_group_self_normalizingproof · cited by 2
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