Оn $p$-supersolvability of a class of finite groups

Let $G$ be a finite group, $H$ a subgroup of $G$ and $H_{sG}$ be the subgroup of $H$ generated by all those subgroups of $H$ which are $s$-permutable in $G.$ Then $H$ is said to be weakly $s$-permutable in $G$ if $G$ has a subnormal subgroup $T$ such that $HT=G$ and $T\cap H\le H_{sG}.$ In the paper the notion of a weakly $s$-permutable subgroup is applied to the study of $p$-supersoluble groups.