This article is cited in 13 papers

Periodic groups saturated by finite simple groups $U_3(2^m)$

D. V. Lytkina^a, L. R. Tukhvatullina^b, K. A. Filippov<sup>b

a</sup> Siberian Fund for Algebra and Logic
^b Krasnoyarsk State Agricultural University

Abstract: Let $\mathfrak M$ be a set of finite groups. A group $G$ is said to be saturated by the groups in $\mathfrak M$ if every finite subgroup of $G$ is contained in a subgroup isomorphic to a member of $\mathfrak M$. It is proved that a periodic group $G$ saturated by groups in a set $\{U_3(2^m)\mid m=1,2,\dots\}$ is isomorphic to $U_3(Q)$ for some locally finite field $Q$ of characteristic 2; in particular, $G$ is locally finite.

Keywords: periodic group, finite group, saturated group.

UDC: 512.542.5

Received: 11.02.2008

 English version: Algebra and Logic, 2008, 47:3, 166–175

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