This article is cited in 1 paper

Mathematical logic, algebra and number theory

On groups saturated with dihedral groups and linear groups of degree $2$

A. A. Shlepkin

Siberian Federal University, pr. Svobodny, 79, 660041, Krasnoyarsk, Russia

Abstract: The paper establishes the structure of periodic groups and Shunkov groups saturated with groups consisting of the groups $\mathfrak{M}$ consisting of the groups $ L_2 (q) $, where $ q\equiv 3,5\pmod{8} $ and dihedral groups with Sylow $2$-subgroup of order $2$. It is proved that a periodic group saturated with groups from $ \mathfrak{M}$ is either isomorphic to a prime Group $ L_2 (Q) $ for some locally-finite field $ Q $, or is isomorphic to a locally dihedral group with Sylow $2$-subgroup of order $2$. Also, the existence of the periodic part of the Shunkov group saturated with groups from the set $ \mathfrak{M} $ is proved, and the structure of this periodic part is established.

Keywords: group saturated with a set of groups.

UDC: 512.54

MSC: 20K01

Received June 29, 2017, published January 30, 2018

DOI: 10.17377/semi.2018.15.009

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