Theorems · Theorem · group theory
AddSubgroup.normal_addSubgroupOf_of_le_normalizer
∀ {G : Type u_1} [inst : AddGroup G] {H N : AddSubgroup G}, H ≤ AddSubgroup.normalizer ↑N → (N.addSubgroupOf H).Normal- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 74 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.
- SetLike.coestatement and proof · cited by 8,199
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- LE.le.transproof · cited by 3,151
- AddSubgroup.Normalstatement · cited by 183
- le_infproof · cited by 107
- AddSubgroup.addSubgroupOfstatement · cited by 87
- AddSubgroup.normalizerstatement and proof · cited by 59
- AddSubgroup.le_normalizerproof · cited by 6
- AddSubgroup.normal_addSubgroupOf_iff_le_normalizer_infproof · cited by 3
- AddSubgroup.inf_normalizer_le_normalizer_infproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.IsSubnormal.mapproof · cited by 1
- QuotientAddGroup.quotientInfEquivSumNormalizerQuotientstatement · cited by 0