One property of hereditary saturated formations

Let $\mathfrak{F}$ be a hereditary saturated formation. 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 $\mathfrak{F}$-subgroup $T$ such that $VT=G$, then $G\in\mathfrak{F}$. Problems 19.87 and 19.88 from the “Kourovka Notebook” are solved in the article.