Theorems · Theorem · group theory
Subgroup.IsSubnormal.normal_of_isSimpleGroup
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G}, IsSimpleGroup G → H.IsSubnormal → H.NormalA subnormal subgroup of a simple 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
- Group
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
- Groupstatement and proof · cited by 6,238
- Bot.botproof · cited by 4,720
- Subgroupstatement and proof · cited by 3,593
- Subgroup.Normalstatement and proof · cited by 334
- Subgroup.subgroupOfproof · cited by 122
- IsSimpleGroupstatement and proof · cited by 26
- Subgroup.IsSubnormalstatement and proof · cited by 19
- Subgroup.Normal.eq_bot_or_eq_topproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.IsSubnormal.eq_bot_or_top_of_isSimpleGroupproof · cited by 0