19.39 (2018)

A group is said to be $\mathfrak{X}$-critical if it does not belong to $\mathfrak{X}$ but all its proper subgroups belong to $\mathfrak{X}$. Let $\mathfrak{F}$ be a soluble hereditary formation of finite groups for which all $\mathfrak{F}$-critical groups are either groups of prime order or $\mathfrak{U}$-critical groups, where $\mathfrak{U}$ is the formation of all supersoluble finite groups. Must $\mathfrak{F}$ be a saturated formation?