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On finite \(p\)-nilpotent groups. (English) Zbl 1369.20017

Summary: In this paper the structure of a minimal counterexample among the non-\(p\)-nilpotent groups having \(p\)-nilpotent \(p\)-Sylow normalisers is analysed. Several \(p\)-nilpotency criteria and many earlier results follow from our main theorem.

MSC:

20D15 Finite nilpotent groups, \(p\)-groups
20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
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