Geodesic
Finite factored groups with soluble $\mathbb{X}$-subnormal factors
Problemy fiziki, matematiki i tehniki, no. 2 (2019), pp. 76-80.

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We establish new criteria of partial solubility of a finite factored group with restrictions on indices in chains of subgroups from factors to the group. In particular, it is proved that if $A$ and $B$ are soluble subgroups of a group $G$ such that there exist chains from $A$ and $B$ to $G$ in which indices of neighboring non-normal subgroups are either odd or equal to $2$ or $4$ and $G = AB$, then $G$ is soluble.
Keywords: finite group, factored group, generalized subnormal subgroup.
Mots-clés : soluble group 
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     title = {Finite factored groups with soluble $\mathbb{X}$-subnormal factors},
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}
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V. N. Kniahina; I. K. Chirik. Finite factored groups with soluble $\mathbb{X}$-subnormal factors. Problemy fiziki, matematiki i tehniki, no. 2 (2019), pp. 76-80. http://geodesic.mathdoc.fr/item/PFMT_2019_2_a10/

[1] V.S. Monakhov, “Faktorizuemye gruppy s razreshimymi faktorami nechetnykh indeksov”, Issledovanie normalnogo i podgruppovogo stroeniya konechnykh grupp, Nauka i tekhnika, Minsk, 1984, 105–111

[2] V.S. Monakhov, V.N. Kniahina, “Finite group with $\mathbb{P}$-subnormal subgroups”, Ricerche di Matematica, 62:2 (2013), 307–323 | DOI | MR

[3] V.N. Kniahina, V.S. Monakhov, “On supersolvability of finite groups with $\mathbb{P}$-subnormal subgroups”, International Journal of Group Theory, 2:4 (2013), 21–29 | MR | Zbl

[4] V.N. Knyagina, V.S. Monakhov, “Konechnye faktorizuemye gruppy s razreshimymi $\mathbb{P}^2$-subnormalnymi podgruppami”, Sibirskii matematicheskii zhurnal, 54:1 (2013), 77–85 | Zbl

[5] A.F. Vasilev, T.I. Vasileva, V.N. Tyutyanov, “O K$\mathbb{P}$-subnormalnykh podgruppakh konechnykh gruppakh”, Matematicheskie zametki, 95:4 (2014), 517–528 | DOI | Zbl

[6] V.N. Tyutyanov, V.N. Knyagina, “Faktorizatsii konechnykh grupp $r$-razreshimymi podgruppami s zadannymi vlozheniyami”, Ukr. mat. zhurn., 55:10 (2014), 1431–1435

[7] V. Monakhov, V. Kniahina, “Finite factorised groups with partially solvable $\mathbb{P}$-subnormal subgroups”, Lobachevskii Journal of Mathematics, 36:4 (2015), 441–445 | DOI | MR | Zbl

[8] I.K. Chirik, “Konechnye faktorizuemye gruppy s razreshimymi K$\mathbb{P}^2$-subnormalnymi podgruppami”, Matematicheskie zametki, 99:1 (2016), 97–101 | DOI | Zbl

[9] V.S. Monakhov, Vvedenie v teoriyu konechnykh grupp i ikh klassov, Vysheishaya shkola, Minsk, 2006, 207 pp.

[10] R.M. Guralnick, “Subgroups of prime power index in a simple group”, J. Algebra, 81:2 (1983), 304–311 | DOI | MR | Zbl

[11] H. Wielandt, “Subnormalitat in faktorisierten endlichen Gruppen”, J. Algebra, 69 (1981), 305–311 | DOI | MR | Zbl

[12] L.S. Kazarin, “Faktorizatsii konechnykh grupp razreshimymi podgruppami”, Ukr. mat. zhurn., 43:7–8 (1991), 947–950