Theorems · Definition · group theory
NormalizerCondition
(G : Type u_1) → [Group G] → Prop
Every proper subgroup H of G is a proper normal subgroup of the normalizer of H in G.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupproof · cited by 3,593
- Subgroup.normalizerproof · cited by 108
Cited by8
Results whose statement or proof uses this declaration.
- Group.isNilpotent_of_finite_tfaestatement and proof · cited by 2
- normalizerCondition_iff_only_full_group_self_normalizingstatement · cited by 2
- Group.normalizerCondition_of_isNilpotentstatement · cited by 2
- Subgroup.NormalizerCondition.normal_of_coatomstatement and proof · cited by 1
- normalizerCondition_of_isNilpotentstatement · cited by 0
- Sylow.normal_of_normalizerConditionstatement and proof · cited by 0
- isNilpotent_of_finite_tfaestatement · cited by 0
- frattini_nilpotentproof · cited by 0