D. V. Lytkina, A. Kh. Zhurtov, “Finite groups whose maximal subgroups have only soluble proper subgroups”, Сиб. электрон. матем. изв., 2022, том 19, выпуск 1,страницы 237

Математическая логика, алгебра и теория чисел

Finite groups whose maximal subgroups have only soluble proper subgroups

D. V. Lytkina^abc, A. Kh. Zhurtov^d

^a Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
^b Novosibirsk State University, 2, Pirogova str., Novosibirsk, 630090, Russia
^c Siberian State University of telecommunications and information sciences, 86, Kirova str., Novosibirsk, 630102, Russia
^d Kabardin-Balkarian State University, 173, Chernyshevskogo str., Nalchik, 360004, Russia

Аннотация: We give a description of a finite group whose maximal subgroups possess only soluble proper subgroups, which implies the answer to the well-known question on composition factors of finite groups, whose second maximal subgroups are soluble.

Ключевые слова: finite group, maximal subgroup, solubility.

УДК: 512.542

MSC: 20F16

Поступила 7 марта 2022 г., опубликована 8 апреля 2022 г.

Язык публикации: английский

DOI: 10.33048/semi.2022.19.017