Реферат: 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.

Библиографическая ссылка: 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

Оригинальная: 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

Даты:

Поступила в редакцию:	29 окт. 2021 г.
Опубликована online:	2 мая 2023 г.

Идентификаторы БД:

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

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