20.112 (2022)

Let $\mathfrak{F}$ be a hereditary saturated formation and let $w^*\mathfrak{F}$ denote the class of all finite groups $G$ for which $\pi(G) \subseteq \pi(\mathfrak{F})$ and the normalizers of all Sylow subgroups of $G$ are $\mathfrak{F}$-subnormal in $G$. It is known that $w^*\mathfrak{F}$ is a formation. Must $w^*\mathfrak{F}$ be a saturated formation?