vestifmИзвестия Национальной академии наук Беларуси. Серия физико-математических наукProceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series1561-24302524-2415The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"10.29235/1561-2430-2026-62-3-183-192vestifm-914Research ArticleМАТЕМАТИКАMATHEMATICSПроизведения конечных групп с условиями формационной субнормальности на подгруппы факторовProducts of finite groups with conditions of formation subnormality on subgroups of factorsБалычевС. В.BalychevS. V.

Балычев Сергей Владимирович – инженер-программист подготовительных курсов института повышения квалификации и переподготовки

ул. Советская, 104, 246028, Гомель

Sergey V. Balychev – Software Engineer at the Preparatory Courses of the Institute of Advanced Trai ning and Retraining

104, Sovetskaya Str., 246028, Gomel

https://orcid.org/0000-0002-0769-2519МурашкоВ. И.MurashkaV. I.

Мурашко Вячеслав Игоревич – кандидат физико-математических наук, доцент, доцент кафедры алгеб ры и геометрии, ведущий научный сотрудник НИС

ул. Советская, 104, 246028, Гомель

Viachaslau I. Murashka – Ph. D. (Physics and Mathematics), Associate Professor, Associate Professor of the Department of Algebra and Geometry, Leading Researcher of Research Sector

104, Sovetskaya Str., 246028, Gomel

mvimath@yandex.ruГомельский государственный университет имени Франциска СкориныБеларусьFrancisk Skorina Gomel State UniversityBelarus202629092026623183192Copyright © Балычев С.В., Мурашко В.И., 20262026Балычев С.В., Мурашко В.И.Balychev S.V., Murashka V.I.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestifm.belnauka.by/jour/article/view/914

Установлена связь между решением проблемы Шеметкова о Z-насыщенных формациях и изучением классов групп, определяемых системами формационно субнормальных подгрупп. Найден критерий разрешимой (насыщенности сверхрадикальной формации. Доказана сверхрадикальность наследственных S-формаций. Описаны все наследственные формации разрешимых групп F, содержащие всякую группу, представленную в произведение своих подгрупп, все H-подгруппы которых F-субнормальны (K-F-субнормальны), где H – насыщенный гомоморф.

The connection between the solution of Shemetkov’s problem on Z-saturated formations and the study of classes of groups defined by systems of formation subnormal subgroups was established. A criterion for a superradical formation to be solvably saturated was found. The superradicality of hereditary S -formations was proved. All hereditary formations F of solvable groups that contain every group representable as a product of its subgroups, all H-subgroups of which are F-subnormal (or K-F-subnormal), where H is a saturated homomorph, were described.

конечная группасверхрадикальная формацияZ-насыщенная формацияS-формациямультифакторизуемая группаF-субнормальная подгруппаK-F-субнормальная подгруппаfinite groupsuperradical formationZ-saturated formationS -formationmultifactorized groupF-subnormal subgroupK-F-subnormal subgroupРабота выполнена при финансовой поддержке Белорусского республиканского фонда фундаментальных исследований (проект № Ф23PHФM-63).The work was financially supported by the Belarusian Republican Foundation for Fundamental Research (project no. Ф23PHФM-63).ReferencesШеметков, Л. А. Формации алгебраических систем / Л. А. Шеметков, А. Н. Скиба. – М.: Наука, 1989. – 256 c.Shemetkov L. A., Skiba A. N. Formations of Algebraic Systems. Moscow, Nauka Publ., 1989. 256 p. (in Russian).Doerk, K. Finite Soluble Groups / K. Doerk, T. Hawkes. – Berlin; New York: Walter de Gruyter, 1992. – 891 p.Doerk K., Hawkes T. Finite Soluble Groups. Berlin, New York, Walter de Gruyter, 1992. 891 p.Каморников, С. Ф. 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The authors declare that there are no conflicts of interest present.