Theorems · Theorem · group theory
Subgroup.NormalizerCondition.normal_of_coatom
∀ {G : Type u_1} [inst : Group G] (H : Subgroup G), NormalizerCondition G → IsCoatom H → H.NormalIn a group that satisfies the normalizer condition, every maximal subgroup is normal
- Defined in
- Mathlib.Algebra.Group.Subgroup.Order
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Subgroupstatement and proof · cited by 3,593
- Subgroup.Normalstatement · cited by 334
- IsCoatomstatement and proof · cited by 114
- Subgroup.normalizerproof · cited by 108
- lt_top_iff_ne_topproof · cited by 95
- Subgroup.normalizer_eq_top_iffproof · cited by 10
- NormalizerConditionstatement and proof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- Group.isNilpotent_of_finite_tfaeproof · cited by 2