Theorems · Theorem · group theory
AddSubgroup.normal_addSubgroupOf_iff_le_normalizer_inf
∀ {G : Type u_1} [inst : AddGroup G] {H K : AddSubgroup G},
(H.addSubgroupOf K).Normal ↔ K ≤ AddSubgroup.normalizer ↑(H ⊓ K)- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 73 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coestatement · cited by 8,199
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- inf_le_rightproof · cited by 238
- AddSubgroup.Normalstatement · cited by 183
- AddSubgroup.addSubgroupOfstatement · cited by 87
- AddSubgroup.normalizerstatement · cited by 59
- AddSubgroup.normal_addSubgroupOf_iff_le_normalizerproof · cited by 8
- AddSubgroup.inf_addSubgroupOf_rightproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- AddSubgroup.normal_addSubgroupOf_of_le_normalizerproof · cited by 1
- AddSubgroup.inf_addSubgroupOf_inf_normal_of_leftproof · cited by 0
- AddSubgroup.inf_addSubgroupOf_inf_normal_of_rightproof · cited by 0