Theorems · Theorem · group theory
AddSubgroup.IsSubnormal.normal_of_isSimpleAddGroup
∀ {G : Type u_1} [inst : AddGroup G] {H : AddSubgroup G}, IsSimpleAddGroup G → H.IsSubnormal → H.NormalA subnormal additive subgroup of a simple additive group is normal.
- Defined in
- Mathlib.GroupTheory.IsSubnormal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 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.
- Top.topproof · cited by 9,680
- Bot.botproof · cited by 4,720
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddSubgroup.Normalstatement and proof · cited by 183
- AddSubgroup.addSubgroupOfproof · cited by 87
- AddSubgroup.IsSubnormalstatement and proof · cited by 17
- IsSimpleAddGroupstatement and proof · cited by 14
- AddSubgroup.Normal.eq_bot_or_eq_topproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.IsSubnormal.eq_bot_or_top_of_isSimpleAddGroupproof · cited by 0