On subgroups lifting modulo central commutant

Abstract

We consider a finitely generated group G with the commutant of odd order $p_1^{n_1 } \ldots p_s^{n_s }$ 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.