Goeters, H. Pat; Ullery, William Quasi-summands of a certain class of Butler groups. (English) Zbl 0806.20043 Fuchs, Laszlo (ed.) et al., Abelian groups. Proceedings of the 1991 Curaçao conference. New York: Marcel Dekker, Inc.. Lect. Notes Pure Appl. Math. 146, 167-174 (1993). Let \(A_ i\), \(i = 1,\cdots,n\) be non-zero subgroups of the additive group of rationals. The cokernel of the diagonal map \(\Delta: \bigcap_{i = 1}^ n A_ i \to \bigoplus_{i = 1}^ n A_ i\) is said to be an \(AV\)-group, while a \(qAV\)-group is any torsion-free group quasi-isomorphic to an \(AV\)-group. The main result of the paper (Th. 2) asserts that the class of \(qAV\)-groups is closed under quasi-summands. The \({\mathcal B}^{(1)}\)-groups in the sense of L. Fuchs, C. Metelli [Manuscr. Math. 71, 1-28 (1991; Zbl 0765.20026)] (\({\mathcal B}^{(1)}\)- groups are just torsion-free factor-groups of finite rank completely decomposable groups by rank one pure subgroups) are closely related to the \(qAV\)-groups and consequently the above result solves in the affirmative the problem whether the quasi-summands of \({\mathcal B}^{(1)}\)- groups are quasi-isomorphic to \({\mathcal B}^{(1)}\)-groups.For the entire collection see [Zbl 0778.00023]. Reviewer: L.Bican (Praha) Cited in 1 Document MSC: 20K15 Torsion-free groups, finite rank 20K25 Direct sums, direct products, etc. for abelian groups 20K27 Subgroups of abelian groups Keywords:\(qAV\)-groups; closed under quasi-summands; finite rank completely decomposable groups; pure subgroups; torsion-free factor-groups Citations:Zbl 0765.20026 PDFBibTeX XMLCite \textit{H. P. Goeters} and \textit{W. Ullery}, Lect. Notes Pure Appl. Math. 146, 167--174 (1993; Zbl 0806.20043)