A note on intersections of some maximal subgroups of finite groups
Problemy fiziki, matematiki i tehniki, no. 2 (2012), pp. 62-64.

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In the work V.S.Monahov's results that for any soluble non-nilpotent finite group $G$ its Frattini subgroup $\Phi(G)$ (subgroup $\Delta(G)$) coincides with intersection of all maximal (respectively all abnormal maximal) subgroups $M$ of group $G$ such that $MF(G) = G$, are extended on arbitrary finite groups.
Keywords: finite group, maximal subgroup, Frattini subgroup, Frattini $\theta$-subgroup, subgroup m-functor.
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A. F. Vasil'ev; T. I. Vasilyeva; A. V. Syrokvashin. A note on intersections of some maximal subgroups of finite groups. Problemy fiziki, matematiki i tehniki, no. 2 (2012), pp. 62-64. http://geodesic.mathdoc.fr/item/PFMT_2012_2_a9/

[1] G. Frattini, “Intorno alla generasione dei gruppi di operazioni”, Atti Acad. dei Lincei, 1 (1885), 281–285

[2] W. Gaschütz, “Über die $\Phi$-Untergruppen endlicher Gruppen”, Math. Z., 58 (1953), 160–170 | DOI | MR

[3] V. S. Monakhov, “Zamechanie o maksimalnykh podgruppakh konechnykh grupp”, Dokl. NAN Belarusi, 47:4 (2003), 31–33 | MR | Zbl

[4] V. S. Monakhov, “Zamechanie o peresechenii nenormalnykh maksimalnykh podgrupp konechnykh grupp”, Izvestiya GGU im. F. Skoriny, 2004, no. 6 (27), 81 | MR

[5] S. F. Kamornikov, M. V. Selkin, Podgruppovye funktory i klassy konechnykh grupp, Bel. navuka, Mn., 2003, 254 pp.

[6] L. A. Shemetkov, Formatsii konechnykh grupp, Nauka, M., 1978, 272 pp. | MR | Zbl

[7] K. Doerk, T. Hawkes, Finite soluble groups, Walter de Gruyter, Berlin–New York, 1992, 891 pp. | MR

[8] M. V. Selkin, R. V. Borodich, “O peresechenii maksimalnykh podgrupp konechnykh grupp”, Vestnik SamGU. Estestvenno-nauchnaya ser., 2009, no. 8 (74), 67–76

[9] B. Huppert, N. Blackburn, Finite groups, v. III, Springer, Berlin–Heidelberg–New York, 1982, 458 pp.

[10] R. Griss, P. Schmid, “The Frattini module”, Arch. Math., 30:3 (1978), 256–266 | DOI | MR