Geodesic
On intersection of abnormal subgroups that don't contain a $\mathfrak{F}$-residual
Problemy fiziki, matematiki i tehniki, no. 1 (2019), pp. 26-30.

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The structure of a subgroup equal to the intersection of maximal $A$-admissible $\Theta$-subgroups not containing the $\mathfrak{F}$-residual is investigated. The influence of the corresponding generalized subgroup Frattini on the structure of the group itself is determined.
Keywords: finite group, abnormal subgroup, $\mathfrak{F}$-residual. 
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R. V. Borodich. On intersection of abnormal subgroups that don't contain a $\mathfrak{F}$-residual. Problemy fiziki, matematiki i tehniki, no. 1 (2019), pp. 26-30. http://geodesic.mathdoc.fr/item/PFMT_2019_1_a4/

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

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

[3] W.E. Deskins, “A condition for the solvability of a finite group”, Ill. J. Math., 5:2 (1961), 306–313 | DOI | MR | Zbl

[4] L.A. Shemetkov, Formatsii konechnykh grupp, Nauka, M., 1978, 267 pp.

[5] M.V. Selkin, Maksimalnye podgruppy v teorii klassov konechnykh grupp, Belaruskaya navuka, Mn., 1997, 144 pp.

[6] A.N. Skiba, Algebra formatsii, Belaruskaya navuka, Mn., 1997, 240 pp.

[7] R.V. Borodich, E.N. Borodich, M.V. Selkin, “Ob $\mathfrak{F}$-dostizhimykh podgruppakh v gruppakh s operatorami”, Problemy fiziki, matematiki i tekhniki, 2015, no. 2 (23), 33–39

[8] R.V. Borodich, E.N. Borodich, “O peresechenii $\mathfrak{F}$-abnormalnykh maksimalnykh $\theta$-podgrupp”, Vestsi NAN Belarusi. Ceryya fiz.-mat. navuk, 2007, no. 3, 47–52

[9] R.V. Borodich, E.N. Borodich, M.V. Selkin, “O peresechenii $A$-dopustimykh $\theta$-podgrupp, ne soderzhaschikh podgruppu Fittinga”, Problemy fiziki, matematiki i tekhniki, 2017, no. 4 (31), 44–47

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

[11] D. Gorenshtein, Finite groups, Harper and Row, New York, 1968, 572 pp. | MR