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\(S\)-semiembedded subgroups of finite groups. (English) Zbl 1328.20040
Summary: A subgroup \(H\) of a finite group \(G\) is said to be \(s\)-semipermutable in \(G\) if it is permutable with every Sylow \(p\)-subgroup of \(G\) with \((p,|H|)=1\). We say that a subgroup \(H\) of a finite group \(G\) is \(S\)-semiembedded in \(G\) if there exists an \(s\)-permutable subgroup \(T\) of \(G\) such that \(TH\) is \(s\)-permutable in \(G\) and \(T\cap H\leqslant H_{\overline sG}\), where \(H_{\overline sG}\) is an \(s\)-semipermutable subgroup of \(G\) contained in \(H\). In this paper, we investigate the influence of \(S\)-semiembedded subgroups on the structure of finite groups.

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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