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Finite groups with \(sn\)-embedded or \(s\)-embedded subgroups. (English) Zbl 1286.20019
Summary: A number of authors have studied the structure of a finite group \(G\) under the assumption that some subgroups of \(G\) are well located in \(G\). We generalize the notion of \(s\)-permutable and \(s\)-permutably embedded subgroups and we obtain new criteria of \(p\)-nilpotency and supersolvability of groups. We also generalize some known results.

MSC:
20D40 Products of subgroups of abstract finite groups
20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
20D15 Finite nilpotent groups, \(p\)-groups
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