  A subgroup $H$ of a group $G$ is called weakly s-supplemented in $G$ if there
is a subgroup $T$ such that $G=HT$ and $H\cap T\le H_{sG}$, where $H_{sG}$ is
the subgroup of $H$ generated by all those subgroups of $H$ which are
s-permutable in $G$. The influence of primary weakly s-supplemented subgroups
on the structure of finite groups is investigated. An open question promoted by
Skiba is studied and some known results are generalized.
