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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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