17.38 (2010)

A formation $\mathfrak{F}$ is called radical in a class $\mathfrak{H}$ if $\mathfrak{F} \subseteq \mathfrak{H}$ and in every $\mathfrak{H}$-group the product of any two normal $\mathfrak{F}$-subgroups belongs to $\mathfrak{F}$. Let $\mathfrak{M}$ be the class of all saturated hereditary formations of finite groups such that the formation of all finite supersoluble groups is radical in every element of $\mathfrak{M}$. Is it true that $\mathfrak{M}$ has the largest (by inclusion) element?