Geodesic
Groups with Formation Subnormal $2$-Maximal Subgroups
Matematičeskie zametki, Tome 105 (2019) no. 2, pp. 269-277.

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Groups with $\mathfrak X$-subnormal $2$-maximal subgroups are investigated for an arbitrary hereditary formation $\mathfrak X$. In such a group, all proper subgroups have nilpotent $\mathfrak X$-residuals. The cases in which $\mathfrak X=\mathfrak A_1\mathfrak F$ for some hereditary formation $\mathfrak F$ or $\mathfrak X$ is a solvable saturated formation are studied in more detail.
Keywords: finite group, residual, subnormal subgroup.
Mots-clés : formation 
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     author = {V. S. Monakhov},
     title = {Groups with {Formation} {Subnormal} $2${-Maximal} {Subgroups}},
     journal = {Matemati\v{c}eskie zametki},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_105_2_a7/}
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V. S. Monakhov. Groups with Formation Subnormal $2$-Maximal Subgroups. Matematičeskie zametki, Tome 105 (2019) no. 2, pp. 269-277. http://geodesic.mathdoc.fr/item/MZM_2019_105_2_a7/

[1] V. S. Monakhov, Vvedenie v teoriyu konechnykh grupp i ikh klassov, Vysheishaya shkola, Minsk, 2006

[2] K. Doerk, T. Hawkes, Finite Soluble Groups, Walter de Gruyter, Berlin, 1992 | MR

[3] V. S. Monakhov, V. N. Kniahina, “Finite groups with $\mathbb P$-subnormal subgroups”, Ric. Mat., 62:2 (2013), 307–322 | DOI | MR | Zbl

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

[5] V. A. Kovaleva, A. N. Skiba, “Finite soluble groups with all $n$-maximal subgroups $\mathfrak F$-subnormal”, J. Group Theory, 17:2 (2014), 273–290 | MR | Zbl

[6] A. Ballester-Bolinches, L. M. Ezquerro, Classes of Finite Groups, Springer-Verlag, Dordrecht, 2006 | MR | Zbl

[7] V. S. Monakhov, “Podgruppy Shmidta, ikh suschestvovanie i nekotorye prilozheniya”, Pratsi Ukrainskogo matematichnogo kongresu – 2001, Sektsiya 1, In-t matem. NAN Ukraini, Kiiv, 2002, 81–90 | Zbl