11.120 (1990)

Let $\mathfrak{F}$ be a soluble saturated Fitting formation. Is it true that $l_{\mathfrak{F}}(G) \leqslant f(c_{\mathfrak{F}}(G))$, where $c_{\mathfrak{F}}(G)$ is the length of a composition series of some $\mathfrak{F}$-covering subgroup of a finite soluble group $G$? This is Problem 17 in (L. A. Shemetkov, Formations of Finite Groups, Moscow, Nauka, 1978 (Russian)). For the definition of the $\mathfrak{F}$-length $l_{\mathfrak{F}}(G)$, see ibid.