Finite groups with permuted strongly generalized maximal subgroups
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.
Keywords
solvable group, i-maximal subgroup, strongly г-maximal subgroup, normal subgroup, nilpotent group, supersolvable group, Schmidt groupAuthors
| Name | Organization | |
| Gorbatova Yulia V. | Russian Presidential Academy of National Economy and Public Administration | g.julia32@yandex.ru |
References
Finite groups with permuted strongly generalized maximal subgroups | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2022. № 80. DOI: 10.17223/19988621/80/3
