On two classes of finite inseparable \(p\)-groups. (English) Zbl 1336.20021
Summary: A finite group is inseparable, it does not split over any proper nontrivial normal subgroup; that is, if it has no nontrivial semidirect product decompositions. This paper investigates two classes of finite inseparable \(p\)-groups and, for \(p\geq 3\), establishes a necessary and sufficient condition for inseparability.
MSC:
| 20D15 | Finite nilpotent groups, \(p\)-groups |
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