E.V. Zubei. On the solvability of a finite group with seminormal or subnormal Schmidt subgroups of one of its maximal subgroups ... P. 55-61

Vol. 25, no. 1, 2019

A Schmidt group is a finite non-nilpotent group all of whose proper subgroups are nilpotent. A group with a nilpotent maximal subgroup is known to be solvable if the derived subgroup of a Sylow 2-subgroup of a maximal subgroup is contained in the center of the Sylow 2-subgroup. If a maximal subgroup of a group is non-nilpotent, then it has a Schmidt subgroup. The structure of a group and, in particular, its solvability, depend on the properties of Schmidt subgroups of its maximal subgroup. In this paper, we establish the solvability of a finite group such that some Schmidt subgroups of its maximal subgroup are seminormal or subnormal in the group.

Keywords: finite group, solvable group, Schmidt subgroup, subnormal subgroup, seminormal subgroup, maximal subgroup

Received December 12, 2018

Revised January 30, 2019

Accepted February 4, 2019

Ekaterina Vladimirovna Zubei, doctoral student, Francisk Skorina Gomel State University, Gomel, 246019, Republic of Belarus, e-mail: ekaterina.zubey@yandex.ru

Cite this article as:   E.V. Zubei. On the solvability of a finite group with seminormal or subnormal Schmidt subgroups of one of its maximal subgroups , Trudy Instituta Matematiki i Mekhaniki URO RAN, 2019, vol. 25, no. 1, pp. 55–61. 


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