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Weakly \(SS\)-quasinormally supplemented subgroups of finite groups. (Chinese. English summary) Zbl 1289.20036

Summary: A subgroup \(H\) of a group \(G\) is said to be weakly \(SS\)-quasinormally supplemented in \(G\) if there is a subgroup \(T\) of \(G\) such that \(G=HT\) and \(H\cap T\leqslant H_{SSG}\), where \(H_{SSG}\) is some \(SS\)-quasinormal subgroup of \(G\) contained in \(H\). By using the concept of weakly \(SS\)-quasinormally supplemented subgroups, some new criteria of \(p\)-nilpotent groups and nilpotent groups are obtained.

MSC:

20D40 Products of subgroups of abstract finite groups
20D25 Special subgroups (Frattini, Fitting, etc.)
20D15 Finite nilpotent groups, \(p\)-groups
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