Groups with finite rank elements

With the aid of the notion of the rank of an element in an arbitrary group, we prove a criterion for an infinite group to be nonsimple and find conditions under which a q-biprimitively finite group G with Chernikov Sylow q-subgroups has a Chernikov quotient group G/O_p(G).Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 6, pp. 836–839, June, 1992.