This article is cited in 27 papers

Periodic groups saturated with the groups $L_2(p^n)$

A. G. Rubashkin, K. A. Filippov

Krasnoyarsk State Agricultural University

Abstract: Given an indexing set $I$ and a finite field $K_\alpha$ for each $\alpha\in I$, $\mathfrak R=\{L_2(K_\alpha)|\alpha\in I\}$ and $\mathfrak N=\{SL_2(K_\alpha)|\alpha\in I\}$. We prove that each periodic group $G$ saturated with groups in $\mathfrak R(\mathfrak N)$ is isomorphic to $L_2(P)$ (respectively $SL_2(P)$) for a suitable locally finite field $P$.

Keywords: saturation, periodic group.

UDC: 512.54

Received: 24.04.2005

 English version: Siberian Mathematical Journal, 2005, 46:6, 1119–1122

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