Clorinda De Vivo, Claudia Metelli
On direct sums of $\text {B}^{(1)}$-groups --- II

Comment.Math.Univ.Carolin. 47,2 (2006) 189-202.

Abstract:$B^{(1)}$-groups are a class of torsionfree Abelian groups of finite rank, part of the main class of Butler groups. In the paper C. Metelli, {On direct sums of $B^{(1)}$-groups}, Comment. Math. Univ. Carolinae {34} (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 indecomposable direct summands of $B^{(1)}$-groups.

Keywords: Butler group, $B^{(1)}$-group, tent, direct decomposition, finite algorithm
AMS Subject Classification: 20K15

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