Geodesic
Finite groups with permuted strongly generalized maximal subgroups
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 80 (2022), pp. 26-38 Cet article a éte moissonné depuis la source Math-Net.Ru

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The structure of finite groups in which any strictly 2-maximal subgroup permutes with an arbitrary strictly 3-maximal subgroup is described. It is shown that the class of groups with this property coincides with the class of groups in which any 2-maximal subgroup permutes with an arbitrary 3-maximal subgroup, and, as a consequence, such groups are solvable. As auxiliary results, we describe the structure of groups in which any strictly 2-maximal subgroup permutes with an arbitrary maximal subgroup. In particular, it is shown that the class of such groups coincides with the class of groups in which any 2-maximal subgroup commutes with all maximal subgroups, and, as a consequence, such groups are supersoluble.
Mots-clés : solvable group, supersolvable group
Keywords: $i$-maximal subgroup, strongly $i$-maximal subgroup, normal subgroup, nilpotent group, Schmidt group. 
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     author = {Yu. V. Gorbatova},
     title = {Finite groups with permuted strongly generalized maximal subgroups},
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     url = {http://geodesic.mathdoc.fr/item/VTGU_2022_80_a2/}
}
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Yu. V. Gorbatova. Finite groups with permuted strongly generalized maximal subgroups. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 80 (2022), pp. 26-38. http://geodesic.mathdoc.fr/item/VTGU_2022_80_a2/

[1] Guo W., Legchekowa H. V., Skiba A. N., “The structure of finite non-nilpotent groups in which every 2-maximal subgroup permutes with all 3-maximal subgroups”, Communications in Algebra, 37:7 (2009), 2446–2456 | DOI | MR

[2] Go V., Legchekova E. V., Skiba A. N., “Konechnye gruppy, v kotorykh lyubaya 3-maksimalnaya podgruppa perestanovochna so vsemi maksimalnymi podgruppami”, Matematicheskie zametki, 86:3 (2009), 350–359 | DOI | MR

[3] Lutsenko (Gorbatova) Yu.V., Go V., Skiba A. N., “O nenilpotentnykh gruppakh, lyubye dve 3-maksimalnye podgruppy kotorykh perestanovochny”, Sibirskii matematicheskii zhurnal, 50:6 (2009), 1255–1268 | DOI | MR

[4] Gorbatova Yu. V., “O perestanovochnykh strogo 2-maksimalnykh i strogo 3-maksimalnykh podgruppakh”, Vestnik rossiiskikh universitetov. Matematika, 26:134 (2021), 121–129 | DOI

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

[6] Shemetkov L. A., Formatsii konechnykh grupp, Nauka, M., 1978, 272 pp. | MR

[7] Lutsenko Yu. V., Skiba A. N., “Konechnye nenilpotentnye gruppy s normalnymi ili $S$-kvazinormalnymi $n$-maksimalnymi podgruppami”, Izvestiya Gomelskogo gosudarstvennogo universiteta im. F. Skoriny, 52:1 (2009), 134–138 | MR

[8] Doerk K., Hawkes T., Finite Soluble Groups, Walter de Gruyter, Berlin-New York, 1992, 889 pp. | MR

[9] Huppert B., Endliche Gruppen, v. I, Springer, Berlin-Heidelberg-New York, 1967, 793 pp. | MR