15.98 (2002)

Let $\mathfrak{F}$ be a saturated formation, and $G$ a finite soluble minimal non-$\mathfrak{F}$-group such that $G^\mathfrak{F}$ is a Sylow $p$-subgroup of $G$. Is it true that $G^\mathfrak{F}$ is isomorphic to a factor group of the Sylow $p$-subgroup of $\text{PSU}(3, p^{2n})$? This is true for the formation of finite nilpotent groups (V. D. Mazurov, S. A. Syskin, Math. Notes, 14, no. 2 (1973), 683–686; A. Kh. Zhurtov, S. A. Syskin, Siberian Math. J., 26, no. 2 (1987), 235–239).