Theorems · Theorem · group theory
Subgroup.IsSubnormal.exists_normal_and_le_and_lt_top_of_ne
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G}, H.IsSubnormal → H ≠ ⊤ → ∃ K, K.Normal ∧ H ≤ K ∧ K < ⊤A proper subnormal subgroup is contained in a proper normal subgroup.
- Defined in
- Mathlib.GroupTheory.IsSubnormal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- le_rflproof · cited by 1,558
- eq_or_neproof · cited by 1,117
- Subgroup.Normalstatement and proof · cited by 334
- top_le_iffproof · cited by 175
- Ne.lt_topproof · cited by 161
- Subgroup.subgroupOfproof · cited by 122
- Subgroup.IsSubnormalstatement and proof · cited by 19
- Subgroup.normalizer_eq_top_iffproof · cited by 10
- Subgroup.normal_subgroupOf_iff_le_normalizerproof · cited by 9
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