11.24 (1990)

A Fitting class $\mathfrak{F}$ is said to be local if there exists a group function $f$ (for definition see (L. A. Shemetkov, Formations of Finite Groups, Moscow, Nauka, 1978 (Russian)) such that $f(p)$ is a Fitting class for every prime number $p$ and
$$\mathfrak{F} = \mathfrak{G}_{\pi(\mathfrak{F})} \cap \bigcap_{p \in \pi(\mathfrak{F})} f(p) \mathfrak{N}_p \mathfrak{G}_{p'}.$$ Is every hereditary Fitting class of finite groups local?