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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)

MSC:

20K15 Torsion-free groups, finite rank
20K25 Direct sums, direct products, etc. for abelian groups
20K27 Subgroups of abelian groups

Citations:

Zbl 0765.20026
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