On Butler $B(2)$-groups decomposing over two base elements

Clorinda de Vivo; Claudia Metelli

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On direct sums of $B^{(1)}$ -groups – II

Clorinda De Vivo, Claudia Metelli (2006)

Commentationes Mathematicae Universitatis Carolinae

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$B^{(1)}$ -groups are a class of torsionfree Abelian groups of finite rank, part of the main class of Butler groups. In the paper C. Metelli, , Comment. Math. Univ. Carolinae (1993), 587–591, the problem of direct sums of $B^{(1)}$ -groups was discussed, and a necessary and sufficient condition was given for the direct sum of two $B^{(1)}$ -groups to be a $B^{(1)}$ -group. While sufficiency holds, necessity was wrongly claimed; we solve here the problem, and in the process study a curious hierarchy among...