On the intersections of the maximal $\theta_\pi$-subgroups of finite groups and a subgroup $\mathfrak{F}$-abnormally $\pi'$-full $m$-functor

Conditions under which for a finite group $G$, a non-empty radical (radical local) formation $\mathfrak{F}$ and a subgroup $m$-functor $\theta$ $\Phi_{\theta_\pi,\overline{G_{\mathfrak{F}}}}(G)=\Phi_{\theta_\pi}(G)\ne G$, $\pi$ — a set of primes, are investigated. The results include, as a consequence, statements on the intersections of the corresponding maximal $\theta$-subgroups without restrictions on their indexes.