Abstract:A necessary and sufficient condition is given for the direct sum of two $\Cal B^{(1)}$-groups to be (quasi-isomorphic to) a $\Cal B^{(1)}$-group. A $\Cal B^{(1)}$-group is a torsionfree Abelian group that can be realized as the quotient of a finite direct sum of rank 1 groups modulo a pure subgroup of rank 1.
Keywords: $\Cal B^{(1)}$-groups, Butler groups of finite rank
AMS Subject Classification: 20K15