Theorems · Theorem · group theory
Subgroup.normalizer_eq_top_iff
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G}, Subgroup.normalizer ↑H = ⊤ ↔ H.Normal- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 69 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- SetLike.coestatement and proof · 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
- eq_top_iffproof · cited by 236
- Subgroup.normalizerstatement and proof · cited by 108
- inv_mul_cancel_leftproof · cited by 88
- Subgroup.Normal.conj_memproof · cited by 23
- Subgroup.mem_topproof · cited by 20
- Subgroup.Normal.mem_comm_iffproof · cited by 4
Cited by10
Results whose statement or proof uses this declaration.
- Subgroup.normal_subgroupOf_iff_le_normalizerproof · cited by 9
- Subgroup.normalizer_eq_topproof · cited by 8
- Subgroup.Normal.mapproof · cited by 4
- Subgroup.normal_comap_iff_of_surjectiveproof · cited by 1
- Subgroup.NormalizerCondition.normal_of_coatomproof · cited by 1
- Sylow.normal_of_all_max_subgroups_normalproof · cited by 1
- Sylow.normal_of_normalizer_normalproof · cited by 1
- Subgroup.IsSubnormal.exists_normal_and_le_and_lt_top_of_neproof · cited by 0
- Sylow.normal_of_normalizerConditionproof · cited by 0
- frattini_nilpotentproof · cited by 0