Geodesic
Intersections of maximal subgroups in a finite group in connection with the local formations and a generally abnormally full subgroup $m$-functor
Problemy fiziki, matematiki i tehniki, no. 2 (2017), pp. 31-39.

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Let $\pi$ be a set of primes. The sufficient conditions that must satisfy a local formation $\mathfrak{F}=\mathfrak{G}_{\pi}\mathfrak{F}$, a finite group $G$ and a subgroup $m$-functor $\theta$, under which $\overline{\Delta}_{\pi}^{\mathfrak{F}}(G)=\Phi_{\theta_{\pi}}^{\mathfrak{F}}(G)=\Delta_{\pi}^{\mathfrak{F}}(G)\in\mathfrak{F}$ also $\overline{\Delta}_{\pi,\overline{G_{\mathfrak{F}}}}^{\mathfrak{F}}(G)=\Phi_{\theta_{\pi},\overline{G_{\mathfrak{F}}}}^{\mathfrak{F}}(G)=\Phi_{\theta_{\pi}}^{\mathfrak{F}}(G)=\Delta_{\pi}^{\mathfrak{F}}(G)\subset G_{\mathfrak{F}}\subset G$, if $\mathfrak{F}=\mathfrak{G}_{\pi}\mathfrak{F}$ is radical, are achieved. As the consequences of the main results there were obtained the assertions for $\pi=\varnothing$ and corresponding local formations.
Keywords: maximal subgroups of finite groups, local and local radical formations, subgroup $m$-functor. 
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L. M. Belokon. Intersections of maximal subgroups in a finite group in connection with the local formations and a generally abnormally full subgroup $m$-functor. Problemy fiziki, matematiki i tehniki, no. 2 (2017), pp. 31-39. http://geodesic.mathdoc.fr/item/PFMT_2017_2_a5/

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