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When is the search of relatively maximal subgroups reduced to quotients? Научная публикация

Журнал

Izvestiya Mathematics
ISSN: 1064-5632

Вых. Данные

Год: 2022, Том: 86, Номер: 6, Страницы: 1102–1122 Страниц : 20 DOI: 10.4213/im9277e

Ключевые слова

finite group, complete class, X -maximal subgroup, Hall subgroup, reduction X -theorem.

Авторы

Го В. ^4,5 , Revin D.O. ^1,2,3

Организации

1	Sobolev Institute of Mathematics Siberian Branch of the Russian Academy of Sciences, Novosibirsk
2	Novosibirsk State University
3	Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
4	School of Science, Hainan University, Haikou, Hainan, P. R. China
5	Department of Mathematics, University of Science and Technology of China, Hefei, P. R. China

Информация о финансировании (2)

1	Институт математики им. С.Л. Соболева СО РАН	FWNF-2022-0002
2	Российский фонд фундаментальных исследований	20-51-00007

Let X be a class of finite groups closed with respect to subgroups, homomorphic images and extensions. Denote by kX(G) the number of conjugacy classes X-maximal subgroups of a finite group G. The natural problem to describe up to conjugacy X-maximal subgroups of a given finite group is complicated by the fact that it is not inductive. In particular, generally speaking, the image of an X-maximal subgroup is not X-maximal in the image of a homomorphism. Nevertheless, there are group homomorphisms which preserve the number of conjugacy classes of X-maximal subgroups (for example, homomorphisms whose kernels are X-groups). With respect to such homomorphisms, the image of an X-maximasubgroup is always X-maximal and, moreover, there is a natural bijection between the conjugacy classes of X-maximal subgroups of the image and preimage. Such homomorphisms are completely described in the paper. More precisely, it is proved that, for a homomorphism ϕ of a group G, the equality kX(G)=kX(imϕ) is satisfied if and only if kX(kerϕ)=1, which in turn is equivalent to the fact that the composition factors of the kernel ϕ belong to an explicitly given list.

Го В. , Revin D.O.
When is the search of relatively maximal subgroups reduced to quotients?
Izvestiya Mathematics. 2022. V.86. N6. P.1102–1122. DOI: 10.4213/im9277e WOS Scopus РИНЦ OpenAlex

Го В. , Ревин Д.О.
Когда поиск относительно максимальных подгрупп редуцируется к факторгруппам?
Известия Российской академии наук. Серия математическая. 2022. Т.86. №6. С.79-100. DOI: 10.4213/im9277 РИНЦ MathNet OpenAlex

Поступила в редакцию:	29 окт. 2021 г.
Принята к публикации:	30 янв. 2022 г.
Опубликована online:	2 мая 2023 г.

Web of science:	WOS:000992259900003
Scopus:	2-s2.0-85165393590
РИНЦ:	59310369
OpenAlex:	W4381306350

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