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Keywords:
finite group; $p$-supersoluble group, $p$-nilpotent group, $\Pi $-property
finite group; $p$-supersoluble group, $p$-nilpotent group, $\Pi $-property
Summary:
Let $H$ be a subgroup of a finite group $G$. We say that $H$ satisfies the $\Pi $-property in $G$ if for any chief factor $L / K$ of $G$, $| G / K : N_{G / K} ( HK/K\cap L/K )|$ is a $\pi (HK/K\cap L/K) $-number. We study the influence of some $p$-subgroups of $G$ satisfying the $\Pi $-property on the structure of $G$, and generalize some known results.
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