Groups, saturated with direct products of the finite simple nonabelian groups

I. V. Sabodakh^a, A. A. Shlepkin<sup>b

a</sup> Krasnoyarsk State Agricultural University, Krasnoyarsk, Russia
^b Siberian Federal University, Krasnoyarsk, Russia

Abstract: In work it is proved, that the periodic group saturated by one group, which is the direct product of finite simple nonabelian groups, is finite, with condition that the centralizer of a Sylow $2$-subgroup of each factor of the direct product doesn’t contain elements of odd order.

Keywords: the periodic group, the direct product of groups, saturation.

UDC: 512.54

Received: 19.11.2011

 English version: Journal of Mathematical Sciences, 2014, 198:5, 621–624