On two problems from “The Kourovka Notebook”

We solve Problems 19.87 and 19.88 formulated by A.N. Skiba in “The Kourovka Notebook.” It is proved that if, for every Sylow subgroup $P$ of a finite group $G$ and every maximal subgroup $V$ of $P$, there is a $\sigma$-soluble ($\sigma$-nilpotent) subgroup $T$ such that $VT=G$, then $G$ is $\sigma$-soluble ($\sigma$-nilpotent, respectively).