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Keywords:
weakly nearly $S$-permutable subgroup; $p$-nilpotent group; supersoluble group; saturated formation
weakly nearly $S$-permutable subgroup; $p$-nilpotent group; supersoluble group; saturated formation
Summary:
Let $G$ be a finite group. A subgroup $H$ of $G$ is called weakly nearly $S$-permutable in $G$ if there exists a normal subgroup $K$ of $G$ such that $G=HK$ and $H\cap K$ is nearly $S$-permutable in $G$. We investigate the influence of primary weakly nearly $S$-permutable subgroups on the structure of group $G$. In particular, some new criteria for a group to be $p$-nilpotent or supersoluble are given.
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