Theorems · Theorem · group theory
Subgroup.normalizer_eq_top
∀ {G : Type u_1} [inst : Group G] (H : Subgroup G) [h : H.Normal], Subgroup.normalizer ↑H = ⊤- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupSubgroup.Normal
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- SetLike.coestatement · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Subgroup.Normalstatement and proof · cited by 334
- Subgroup.normalizerstatement · cited by 108
- Subgroup.normalizer_eq_top_iffproof · cited by 10
Cited by9
Results whose statement or proof uses this declaration.
- Subgroup.Normal.mapproof · cited by 4
- SemidirectProduct.mulEquivSubgroupstatement · cited by 3
- Subgroup.subset_normalizer_of_normalproof · cited by 2
- Sylow.commutator_eq_bot_or_commutator_eq_selfproof · cited by 1
- IsZGroup.isCyclic_commutatorproof · cited by 1
- SemidirectProduct.mulEquivSubgroup_applystatement · cited by 0
- SemidirectProduct.mulEquivSubgroup_symm_applystatement · cited by 0
- isZGroup_iff_exists_mulEquivproof · cited by 0
- Sylow.smul_eq_of_normalproof · cited by 0