12.72 (1992)

Let $\mathfrak{F}$ be a soluble local hereditary formation of finite groups. Prove that $\mathfrak{F}$ is radical if every finite soluble minimal non-$\mathfrak{F}$-group $G$ is a minimal non-$\mathfrak{N}^{l(G)-1}$-group. Here $\mathfrak{N}$ is the formation of all finite nilpotent groups, and $l(G)$ is the nilpotent length of $G$.