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On nearly \(SS\)-embedded subgroups of finite groups. (English) Zbl 1308.20021
Summary: Let \(H\) be a subgroup of a finite group \(G\). \(H\) is nearly \(SS\)-embedded in \(G\) if there exists an \(S\)-quasinormal subgroup \(K\) of \(G\), such that \(HK\) is \(S\)-quasinormal in \(G\) and \(H\cap K\leq H_{\mathrm{se\,}G}\), where \(H_{\mathrm{se\,}G}\) is the subgroup of \(H\), generated by all those subgroups of \(H\) which are \(S\)-quasinormally embedded in \(G\). In this paper, the authors investigate the influence of nearly \(SS\)-embedded 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
20D15 Finite nilpotent groups, \(p\)-groups
20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
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