On subgroups lifting modulo central commutant

We consider a finitely generated group G with the commutant of odd order located at the center and prove that there exists a decomposition of G/G′ into the direct product of indecomposable cyclic groups such that each factor except at most n _l + ... + n _s factors lifts modulo commutant. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 5, pp. 742–745, May, 1998.