Theorems · Theorem · group theory
AddSubgroup.normal_addSubgroupOf_iff_le_normalizer
∀ {G : Type u_1} [inst : AddGroup G] {H K : AddSubgroup G},
H ≤ K → ((H.addSubgroupOf K).Normal ↔ K ≤ AddSubgroup.normalizer ↑H)- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.coestatement · cited by 8,199
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddSubgroup.Normalstatement and proof · cited by 183
- AddSubgroup.addSubgroupOfstatement and proof · cited by 87
- AddSubgroup.normalizerstatement · cited by 59
- AddSubgroup.normalizer_eq_top_iffproof · cited by 6
- AddSubgroup.addSubgroupOf_eq_topproof · cited by 3
- AddSubgroup.addSubgroupOf_normalizer_eqproof · cited by 1
Cited by8
Results whose statement or proof uses this declaration.
- AddSubgroup.normal_addSubgroupOf_iff_le_normalizer_infproof · cited by 3
- AddSubgroup.IsSubnormal.trans'proof · cited by 2
- AddSubgroup.IsSubnormal.comapproof · cited by 1
- AddSubgroup.IsSubnormal.mapproof · cited by 1
- AddSubgroup.le_normalizer_of_normal_addSubgroupOfproof · cited by 0
- AddSubgroup.normal_addSubgroupOf_sup_of_le_normalizerproof · cited by 0
- AddSubgroup.IsSubnormal.exists_normal_and_le_and_lt_top_of_neproof · cited by 0
- AddSubgroup.maximal_normal_addSubgroupOf_normalizerproof · cited by 0