This article is cited in 22 papers

The periodic groups saturated by finitely many finite simple groups

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

a</sup> Novosibirsk State University
^b Krasnoyarsk State Agricultural University

Abstract: Denote by $\mathfrak M$ the set whose elements are the simple 3-dimensional unitary groups $U_3(q)$ and the linear groups $L_3(q)$ over finite fields. We prove that every periodic group, saturated by the groups of a finite subset of $\mathfrak M$, is finite.

Keywords: saturation of a group by a set of groups, periodic group.

UDC: 512.54

Received: 15.11.2007

 English version: Siberian Mathematical Journal, 2008, 49:2, 317–321

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