Giovannitti, Anthony; Goeters, H. Pat; Metelli, Claudia Cobalanced exact sequences. (English) Zbl 0693.20055 Commentat. Math. Univ. Carol. 30, No. 4, 637-641 (1989). An exact sequence of abelian groups E: \(0\to A\to B\to C\to 0\) with C torsion free is balanced if every subgroup of the additive rationals Q is projective with respect to E. Dually, if A is torsion-free, E is called cobalanced if every subgroup of Q is injective with respect to E. A well- known result of Bican and Salce says that a torsion-free finite rank group C is a Butler group (pure subgroup of a finite rank completely decomposable group) if and only if \(Bext(C,T)=0\) for all torsion groups T. This last condition means that every balanced sequence E, with A torsion, is a split exact sequence. In this note the authors study those torsion-free groups A such that \(Cobext(T,A)=0\) for all torsion T (every cobalanced sequence E, with C torsion is split exact). In general, such an A is characterized by the condition: A is isomorphic to a pure subgroup of a product of subgroups of Q. In the countable case, an equivalent condition is that A is locally completely decomposable. Reviewer: C.Vinsonhaler Cited in 1 ReviewCited in 4 Documents MSC: 20K40 Homological and categorical methods for abelian groups 20K15 Torsion-free groups, finite rank 20K20 Torsion-free groups, infinite rank 20K27 Subgroups of abelian groups Keywords:torsion-free finite rank group; Butler group; finite rank completely decomposable group; balanced sequence; split exact sequence; torsion-free groups; cobalanced sequence; pure subgroup; locally completely decomposable PDF BibTeX XML Cite \textit{A. Giovannitti} et al., Commentat. Math. Univ. Carol. 30, No. 4, 637--641 (1989; Zbl 0693.20055) Full Text: EuDML