Geodesic
Submaximal and epimaximal $\mathfrak{X}$-subgroups
Algebra i logika, Tome 58 (2019) no. 6, pp. 714-719.

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We discuss how meaningful is the concept of an epimaximal $\mathfrak{X}$-subgroup dual to the concept of a submaximal $\mathfrak{X}$-subgroup introduced by H. Wielandt. Also a result of Wielandt is refined which characterizes the behavior of maximal $\mathfrak{X}$-subgroups under homomorphisms.
Keywords: finite group, maximal $\mathfrak{X}$-subgroup, submaximal $\mathfrak{X}$-subgroup, epimaximal $\mathfrak{X}$-subgroup. 
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     title = {Submaximal and epimaximal $\mathfrak{X}$-subgroups},
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     url = {http://geodesic.mathdoc.fr/item/AL_2019_58_6_a2/}
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D. O. Revin. Submaximal and epimaximal $\mathfrak{X}$-subgroups. Algebra i logika, Tome 58 (2019) no. 6, pp. 714-719. http://geodesic.mathdoc.fr/item/AL_2019_58_6_a2/

[1] O. Hölder, “Bildung zusammengesetzter Gruppen”, Math. Ann., XLVI (1895), 321–422 | DOI | MR

[2] V. Go, D. O. Revin, “O maksimalnykh i submaksimalnykh ${\mathfrak X}$-podgruppakh”, Algebra i logika, 57:1 (2018), 14–42 | MR | Zbl

[3] H. Wielandt, “Zusammengesetzte Gruppen: Holders Programm heute”, Finite groups (Santa Cruz Conf., 1979), Proc. Symp. Pure Math., 37, Am. Math. Soc., Providence, RI, 1980, 161–173 | DOI | MR | Zbl

[4] H. Wielandt, “Zusammengesetzte Gruppen endlicher Ordnung. Vorlesung an der Univ. Tübingen im Wintersemester 1963/64”: H. Wielandt, Mathematische Werke. Mathematical works, v. 1, Group theory, eds. B. Huppert, H. Schneider, Walter de Gruyter, Berlin, 1994, 607–655 | MR

[5] V. Go, D. O. Revin, “O svyazi mezhdu sopryazhennostyu maksimalnykh i submaksimalnykh ${\mathfrak X}$-podgrupp”, Algebra i logika, 57:3 (2018), 261–278 | MR | Zbl

[6] W. Guo, D. O. Revin, E. P. Vdovin, Finite groups in which the ${\mathfrak X}$-maximal subgroups are conjugate, arXiv: 1808.10107 [math.GR] | MR

[7] P. Hall, “Theorems like Sylow's”, Proc. Lond. Math. Soc., III. Ser., 6 (1956), 286–304 | DOI | MR | Zbl

[8] D. Revin, S. Skresanov, A. Vasil'ev, “The proper definition and Wielandt–Hartley's theorem for submaximal $\mathfrak{X}$-subgroups”, Mon. Math., arXiv: 1910.09785 [math.GR]

[9] W. Guo, D. O. Revin, “Classification and properties of the $\pi$-submaximal subgroups in minimal nonsolvable groups”, Bull. Math. Sci., 8:2 (2018), 325–351 | DOI | MR | Zbl

[10] W. Guo, D. O. Revin, “Pronormality and submaximal ${\mathfrak X}$-subgroups on finite groups”, Commun. Math. Stat., 6:3 (2018), 289–317 | DOI | MR | Zbl

[11] I. N. Belousov, M. S. Nirova, “Mezhdunarodnaya konferentsiya "‘Algebra, teoriya chisel i matematicheskoe modelirovanie dinamicheskikh sistem"’, posvyaschennaya 70-letnemu yubileyu A. Kh. Zhurtova”, Tr. IMM UrO RAN, 25, no. 4, 2019, 283–287