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 Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 74–85 (Mi semr900)

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.

DOI: https://doi.org/10.17377/semi.2018.15.009

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Document Type: Article
UDC: 512.54
MSC: 20K01
Received June 29, 2017, published January 30, 2018

Citation: A. A. Shlepkin, “On groups saturated with dihedral groups and linear groups of degree $2$”, Sib. Èlektron. Mat. Izv., 15 (2018), 74–85

Citation in format AMSBIB
\Bibitem{Shl18} \by A.~A.~Shlepkin \paper On groups saturated with dihedral groups and linear groups of degree~$2$ \jour Sib. \Elektron. Mat. Izv. \yr 2018 \vol 15 \pages 74--85 \mathnet{http://mi.mathnet.ru/semr900} \crossref{https://doi.org/10.17377/semi.2018.15.009} `