danДоклады Национальной академии наук БеларусиDoklady of the National Academy of Sciences of Belarus1561-83232524-2431The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"10.29235/1561-83232023-67-6-460-464dan-1161Research ArticleМАТЕМАТИКАMATHEMATICSО некоторых классах конечных σ-разрешимых PσT-группOn some classes of finite σ-soluble PσT-groupshttps://orcid.org/0000-0001-6896-7208СафоноваИ. Н.SafonovaI. N.

Сафонова Инна Николаевна – канд. физ.-мат. наук, доцент.

Пр. Независимости, 4, 220030, Минск

Safonova Inna N. – Ph. D. (Physics and Mathematics), Associate Professor.

4, Nezavisimosti Ave., 220030, Minsk

in.safonova@mail.ruhttps://orcid.org/0000-0002-6521-2712СкибаА. Н.SkibaA. N.

Скиба Александр Николаевич – д-р физ.-мат. наук, профессор.

Ул. Советская, 104, 246019, Гомель

Skiba Alexander N. – D. Sc. (Physics and Mathematics), Professor.

104, Sovetskaya Str., 246019, Gomel

alexander.skiba49@gmail.comБелорусский государственный университетBelarusian State UniversityГомельский государственный университет им. Франциска СкориныFrancisk Skorina Gomel State University202306012024676460464Copyright © Сафонова И.Н., Скиба А.Н., 20242024Сафонова И.Н., Скиба А.Н.Safonova I.N., Skiba A.N.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://doklady.belnauka.by/jour/article/view/1161

Пусть X – класс групп. Предположим, что каждой группе G ∈ X  сопоставлена некоторая система ее подгрупп τ(G). Тогда говорят, что τ – подгрупповой функтор на , X если выполняются следующие условия: (1) G ∈ τ(G) для каждой группы ; G ∈ X (2) для любого эпиморфизма φ: A→B, где, A,B ∈ X и для любых групп H ∈ τ(A) и T ∈ τ(B) имеем Hφ ∈ τ(B) and Tφ-1∈ τ(A). Рассмотрены некоторые приложения таких подгрупповых функторов в теории конечных групп, у которых транзитивна обобщенная нормальность для подгрупп.

Let X be a class of groups. Suppose that with each group G ∈ X we associate some system of its subgroups τ(G). Then τ is said to be a subgroup functor on X if the following conditions are hold: (1) G ∈  τ(G) for each group G ∈ X; (2) for any epimorphism φ: A → B, where A, B ∈ X, and for any groups H ∈ τ(A) and T ∈ τ(B) we have Hφ ∈ τ(B) and Tφ-1 ∈ τ( A). In this paper, were considered some applications of such subgroup functors in the theory of finite groups in which generalized normality for subgroups is transitive.

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The authors declare that there are no conflicts of interest present.