Theorems · Theorem · group theory
Subgroup.IsSubnormal.eq_bot_or_top_of_isSimpleGroup
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G}, IsSimpleGroup G → H.IsSubnormal → H = ⊥ ∨ H = ⊤A subnormal subgroup of a simple group is either trivial or the whole group.
- Defined in
- Mathlib.GroupTheory.IsSubnormal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- Groupstatement and proof · cited by 6,238
- Bot.botstatement · cited by 4,720
- Subgroupstatement and proof · cited by 3,593
- IsSimpleGroupstatement and proof · cited by 26
- Subgroup.IsSubnormalstatement and proof · cited by 19
- Subgroup.Normal.eq_bot_or_eq_topproof · cited by 7
- Subgroup.IsSubnormal.normal_of_isSimpleGroupproof · cited by 1
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