Theorems · Theorem · group theory
AddSubgroup.normalizer_eq_top_iff
∀ {G : Type u_1} [inst : AddGroup G] {H : AddSubgroup G}, AddSubgroup.normalizer ↑H = ⊤ ↔ H.Normal- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 69 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.
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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- eq_top_iffproof · cited by 236
- AddSubgroup.Normalstatement and proof · cited by 183
- neg_add_cancel_leftproof · cited by 84
- AddSubgroup.normalizerstatement and proof · cited by 59
- AddSubgroup.mem_topproof · cited by 29
- AddSubgroup.Normal.conj_memproof · cited by 16
- AddSubgroup.Normal.mem_comm_iffproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- AddSubgroup.normal_addSubgroupOf_iff_le_normalizerproof · cited by 8
- AddSubgroup.Normal.mapproof · cited by 3
- AddSubgroup.normal_opproof · cited by 3
- AddSubgroup.normal_iff_map_addConj_eqproof · cited by 2
- AddSubgroup.normalizer_eq_topproof · cited by 2
- AddSubgroup.IsSubnormal.exists_normal_and_le_and_lt_top_of_neproof · cited by 0