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Finite \(p\)-groups with a uniqueness condition for non-normal subgroups. (English) Zbl 1084.20016

Summary: We determine up to isomorphism all finite \(p\)-groups \(G\) which possess non-normal subgroups and each non-normal subgroup is contained in exactly one maximal subgroup of \(G\). For \(p=2\) this problem is essentially more difficult and we obtain in that case two new infinite families of finite \(2\)-groups.

MSC:

20D15 Finite nilpotent groups, \(p\)-groups
20D30 Series and lattices of subgroups
20E28 Maximal subgroups
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