Theorems · Theorem · group theory
AddSubgroup.IsSubnormal.exists_normal_and_le_and_lt_top_of_ne
∀ {G : Type u_1} [inst : AddGroup G] {H : AddSubgroup G}, H.IsSubnormal → H ≠ ⊤ → ∃ K, K.Normal ∧ H ≤ K ∧ K < ⊤A proper subnormal additive subgroup is contained in a proper normal additive 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
- AddGroup
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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- le_rflproof · cited by 1,558
- eq_or_neproof · cited by 1,117
- AddSubgroup.Normalstatement and proof · cited by 183
- top_le_iffproof · cited by 175
- Ne.lt_topproof · cited by 161
- AddSubgroup.addSubgroupOfproof · cited by 87
- AddSubgroup.IsSubnormalstatement and proof · cited by 17
- AddSubgroup.normal_addSubgroupOf_iff_le_normalizerproof · cited by 8
- AddSubgroup.normalizer_eq_top_iffproof · cited by 6
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