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Mathematical logic, algebra and number theory

Periodic groups saturated by direct products of the Suzuki's group for elementary abelian 2-groups

A. A. Duzh

Krasnoyarsk State Agricultural University

Abstract: It is proved that a periodic groups saturated by the set of groups $\mathfrak{M} = \{P\times V_n \mid n \in N \}$, where $V_n$ is an elementary abelian 2-group of order $2^{n}$, and $P=Sz(q)$, where $q=2^{2m+1}$, $m$ is a fixed natural number, is isomorphic to $P\times V$, where $V$ is an elementary abelian 2-group.

Keywords: periodic group, saturation.

UDC: 512.54

MSC: 13A99

Received January 24, 2013, published April 23, 2013