Theorems · Theorem · group theory
Subgroup.IsSubnormal.trans
∀ {G : Type u_1} [inst : Group G] {H K : Subgroup G},
H ≤ K → (H.subgroupOf K).IsSubnormal → K.IsSubnormal → H.IsSubnormalIf H is a subnormal subgroup of K and K is a subnormal subgroup of G,
then H is a subnormal subgroup of G.
- Defined in
- Mathlib.GroupTheory.IsSubnormal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 74 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.
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Subgroup.mapproof · cited by 301
- Subgroup.subtypeproof · cited by 185
- Subgroup.subgroupOfstatement and proof · cited by 122
- Subgroup.IsSubnormalstatement and proof · cited by 19
- Subgroup.map_subgroupOf_eq_of_leproof · cited by 4
- Subgroup.IsSubnormal.trans'proof · cited by 2
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