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Abstract
In [14] we established a relationship between genus and localization of finitely generated torsion-free abelian by finite groups aud grnus and localization integral representation theory. In this paper we strrcly the consequences of this relationship. We prove results about the genus of groups which are analogues to results in integral representaion theory. In particular we prove non-cancellation phenomena for finitely generated groups with finite commutator subgroups.