Geodesic
Finite groups with permuted strongly generalized maximal subgroups
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 80 (2022), pp. 26-38

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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. 
@article{VTGU_2022_80_a2,
     author = {Yu. V. Gorbatova},
     title = {Finite groups with permuted strongly generalized maximal subgroups},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {26--38},
     publisher = {mathdoc},
     number = {80},
     year = {2022},
     language = {ru},
     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/