Сибирский федеральный университет

Тип публикации: статья из журнала

Год издания: 2021

Идентификатор DOI: 10.21538/0134-4889-2021-27-1-207-219

Ключевые слова: groups with saturation conditions, shunkov group, periodic part of a group

Аннотация: Let G be a group, and let X be a set of groups. A group G is saturated with groups from the set X if any finite subgroup of G is contained in a subgroup of G isomorphic to some group from X. If all elements of finite orders from G are contained in a perio Let G be a group, and let X be a set of groups. A group G is saturated with groups from the set X if any finite subgroup of G is contained in a subgroup of G isomorphic to some group from X. If all elements of finite orders from G are contained in a periodic subgroup T(G) of G, then T(G) is called the periodic part of G. A group G is called a Shunkov group if, for any finite subgroup H of G, in G/N(G) any two conjugate elements of prime order generate a finite group. A Shunkov group may have no periodic part. It is proved that a Shunkov group saturated with finite linear and unitary groups of degree 3 over finite fields of characteristic 2 has a periodic part, which is isomorphic to either a linear or a unitary group of degree 3 over a suitable locally finite field of characteristic 2. © 2021 Krasovskii Institute of Mathematics and Mechanics. All Rights Reserved.

Журнал: TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN

Выпуск журнала: Vol. 27, Is. 1

Номера страниц: 207-219

ISSN журнала: 01344889

Место издания: YEKATERINBURG

Издатель: KRASOVSKII INST MATHEMATICS & MECHANICS URAL BRANCH RUSSIAN ACAD SCIENCES

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

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