Let $\mathfrak{F}$ be a saturated formation containing all supersolvable groups and $G$ a group with a normal subgroup $E$ such that $G/E \in \mathfrak{F}$. Suppose that every non-cyclic Sylow subgroup $P$ of $E$ (or $F^*(E)$) has a subgroup $D$ such that $1 < |D| < |P|$. A question proposed by A. N. Skiba is: does  it $G \in \mathfrak{F}$ hold if all subgroups $H$ of $P$ with order

$|H| = |D|$ and with order $2|D|$ (if $P$ is a non-abelian 2-group and $[P:D]> 2$) are weakly s-supplemented in $G$?  In this talk, we focus on this question and some properties of finite groups are discussed.