Сибирский федеральный университет

Тип публикации: научное издание

Год издания: 2020

Идентификатор DOI: 10.26516/1997-7670.2020.31.132

Ключевые слова: a periodic group; Shunkov group; groups saturated with a given set of groups; strongly embedded subgroup; Bender's theorem, a periodic group, bender's theorem, groups saturated with a given set of groups, shunkov group, strongly embedded subgroupby the russian science foundation

Аннотация: An important concept in the th#331: eory of finite groups is the concept of a strongly embedded subgroup. The fundamental result on the structure of finite groups with a strongly embedded subgroup belongs to M. Suzuki. A complete classification of finite groups with a strongly embedded subgroup was obtained by G. Bender. Infinite periodic groups with a strongly embedded subgroup were first investigated by V. P. Shunkov and A. N. Izmailov under certain restrictions on the groups in question. The structure of a periodic group with a strongly embedded subgroup saturated with finite simple non-abelian groups is developed. The concepts of a strongly embedded subgroup and a group saturated with a given set of groups do not imply the periodicity of the original group. In this connection, the question arises of the location of elements of finite order both in groups with a strongly embedded subgroup and in groups saturated with some set of groups. One of the interesting classes of mixed groups (i.e., groups containing both elements of finite order and elements of infinite order) is the class of Shunkov groups. It is proved that a Shunkov group with a strongly embedded subgroup saturated with finite simple non-abelian groups has a periodic part.

Журнал: BULLETIN OF IRKUTSK STATE UNIVERSITY-SERIES MATHEMATICS

Выпуск журнала: Vol. 31

Номера страниц: 132-141

ISSN журнала: 19977670

Место издания: IRKUTSK

• Shlepkin A. A. (Siberian Fed Univ, 79 Svobodny Pr, Krasnoyarsk 660041, Russia)

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