On $\Pi$-property of $p$-subgroups and the $p$-supersolvability of Finite Groups
DOI:
https://doi.org/10.29020/nybg.ejpam.v19i1.6616Keywords:
Finite group, $\Pi$-property, $p$-supersolvableAbstract
A subgroup $H$ of a group $G$ is said to satisfy $\Pi$-property in $G$ such that for any $G$-chief factor $U/V$, $|G/V:N_{G/V}(HV/V\cap U/V)|$ is a $\pi(HV/V\cap U/V)$-number. In this paper, we present a new criterion for $p$-supersolvability of finite groups by using of a small quantity of maximal subgroups of a Sylow $p$-subgroup satisfying the $\Pi$-property. As applications, we obtain some sufficient conditions for a finite group to be $p$-nilpotent and supersolvable. A number of known results are improved and extended.
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Copyright (c) 2026 Jiawen He, Huaquan Wei, Hui Wu, Liying Yang
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