Geodesic
On the supersolubility of a group with given systems of conditionally seminormal subgroups
Trudy Instituta matematiki, Tome 31 (2023) no. 2, pp. 81-90.

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The subgroups $A$ and $B$ are said to be $\mathrm{cc}$-permutable, if $A$ is permutable with $B^x$ for some ${x\in \langle A,B\rangle}$. A subgroup $A$ of a finite group $G$ is called conditionally seminormal subgroup in $G$, if there exists a subgroup $T$ of $G$ such that $G=AT$ and $A$ is $\mathrm{cc}$-permutable with all subgroups of $T$. In this paper, we proved the supersolubility of a group $G = AB$, where $A$ and $B$ are supersoluble conditionally seminormal subgroups in $G$, in the following cases: the derived subgroup $G^\prime$ is nilpotent; ${(|A|,|B|)=1}$; $G$ is metanilpotent and ${(|G:A|,|G:B|)=1}$; $G$ is metanilpotent and ${(|A/A^{\frak N}|,|B/B^{\frak N}|)=1}$. Besides, we obtained the supersolubility of a group in which maximal subgroups, Sylow subgroups, maximal subgroups of every Sylow subgroup, minimal subgroups, $2$-maximal subgroups are conditionally seminormal subgroups. 
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A. A. Trofimuk. On the supersolubility of a group with given systems of conditionally seminormal subgroups. Trudy Instituta matematiki, Tome 31 (2023) no. 2, pp. 81-90. http://geodesic.mathdoc.fr/item/TIMB_2023_31_2_a8/

[1] Guo W., Shum K. P., Skiba A. N., “Conditionally permutable subgroups and supersolubility of finite groups”, Southeast Asian Bull. Math., 29 (2005), 493–510 | MR | Zbl

[2] Asaad M., Shaalan A., “On the supersolubility of finite groups”, Arch. Math., 53 (1989), 318–326 | DOI | MR | Zbl

[3] Ballester-Bolinches A., Estaban-Romero R., Asaad M., Products of finite groups, Walter de Gruyter, Berlin, 2010 | MR | Zbl

[4] Trofimuk A. A., “On the supersol4ubility of a group with some tcc-subgroups”, J. Algebra Appl, 20:2 (2021), 2150020-1–2150020-18 | DOI | MR

[5] Guo W., Shum K. P., Skiba A. N., “Criterions of supersolubility for products of supersoluble groups”, Publ. Math. Debrecen, 68:3–4 (2006), 433–449 | DOI | MR | Zbl

[6] Monakhov V. S., Trofimuk A. A., “O sverkhrazreshimosti gruppy s polunormalnymi podgruppami”, Sib. mat. zhurn., 61:1 (2020), 148–159 | MR | Zbl

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

[8] Huppert B., Endliche Gruppen I, Springer, Berlin–Heidelberg–New York, 1967 | MR | Zbl

[9] Monakhov V. S., Chirik I. K., “O sverkhrazreshimom koradikale proizvedeniya subnormalnykh sverkhrazreshimykh podgrupp”, Sib. mat. zhurn., 58:2 (2017), 353–364 | MR | Zbl

[10] Doerk K., “Minimal nichtüberauflösbare, endliche gruppen”, Math. Zeitschrift, 91 (1966), 198–205 | DOI | MR | Zbl

[11] Wielandt H., “Subnormalität in faktorisierten endlichen Gruppen”, J. Algebra, 69:2 (1981), 305–311 | DOI | MR | Zbl

[12] Baer R., “Supersoluble immersion”, Can. J. Math., 11 (1959), 353–369 | DOI | MR | Zbl

[13] A system for computational discrete algebra GAP 4.12.2 (Date of access: 22.09.2023) https://www.gap-system.org

[14] Tyutyanov V. N., Kniahina V. N., “Finite groups with biprimary Hall subgroups”, J. Algebra, 443 (2015), 430–440 | DOI | MR | Zbl

[15] Monakhov V. S., Trofimuk A. A., “On the supersolubility of a finite group with NS-supplemented subgroups”, Acta Math. Hungar, 160:1 (2020), 161–167 | DOI | MR | Zbl