Abstract
Groups with X-subnormal 2-maximal subgroups are investigated for an arbitrary hereditary formation X. In such a group, all proper subgroups have nilpotent X-residuals. The cases in which X = A1F for some hereditary formation F or X is a solvable saturated formation are studied in more detail.
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References
V. S. Monakhov, Introduction to the Theory of Finite Groups and Their Classes (Vysh. Shkola, Minsk, 2006) [in Russian].
K. Doerk and T. Hawkes, Finite Soluble Groups (Walter de Gruyter, Berlin, 1992).
V. S. Monakhov and V. N. Kniahina, “Finite groups with P–subnormal subgroups,” Ric. Mat. 62 (2), 307–322 (2013).
L. A. Shemetkov, Formations of Finite Groups (Nauka, Moscow, 1978) [in Russian].
V. A. Kovaleva and A. N. Skiba, “Finite soluble groups with all n–maximal subgroups F–subnormal,” J. Group Theory 17 (2), 273–290 (2014).
A. Ballester–Bolinches and L. M. Ezquerro, Classes of Finite Groups (Springer–Verlag, Dordrecht, 2006).
V. S. Monakhov, “Schmidt subgroups, their existence and some applications,” in Ukrainian Mathematics Congress–2001 (Natsional. Akad. Nauk Ukraini, Inst. Mat., Kiev, 2002), Sec. 1, pp. 81–90 [in Russian].
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Russian Text © V. S. Monakhov, 2019, published in Matematicheskie Zametki, 2019, Vol. 105, No. 2, pp. 269–277.
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Monakhov, V.S. Groups with Formation Subnormal 2-Maximal Subgroups. Math Notes 105, 251–257 (2019). https://doi.org/10.1134/S0001434619010279
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DOI: https://doi.org/10.1134/S0001434619010279