On \(p\)-supersolubility of one class finite groups. (English) Zbl 1429.20003
Summary: The following is proved: A finite group \(G\) is \(p\)-supersoluble if and only if it has a normal subgroup \(N\) with \(p\)-supersoluble quotient \(G / N\) such that either \(N\) is \(p'\)-group or \(p\) divides \(|N|\) and \(|G : N_G(L)|\) equals to a power of \(p\) for any cyclic \(p\)-subgroup \(L\) of \(N\) of order \(p\) or order \(4\) (if \(p = 2\) and a Sylow \(2\)-subgroup of \(N\) is non-abelian).
MSC:
| 20D10 | Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks |
| 20D15 | Finite nilpotent groups, \(p\)-groups |
| 20D20 | Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure |
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