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Finite groups with given normalizers of Sylow subgroups. II. (Chinese. English summary) Zbl 0862.20014

Summary: [For part I cf. Chin. Ann. Math., Ser. A 15, No. 6, 627-631 (1994; Zbl 0838.20020).]
In finite soluble groups a necessary and sufficient condition is obtained for an \(S\)-closed local formation \(\mathfrak F\) with \(m({\mathfrak F})\leq 2\) to have the property: “If the normalizer of any non-unit Sylow subgroup of a group \(G\) belongs to \(\mathfrak F\), then \(G\) belongs to \(\mathfrak F\)”.

MSC:

20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
20D15 Finite nilpotent groups, \(p\)-groups

Citations:

Zbl 0838.20020
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