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Abelian groups with small cotorsion images

1991; Cambridge University Press; Volume: 50; Issue: 2 Linguagem: Inglês

10.1017/s1446788700032729

2396-8192

Rüdiger Göbel,

Rings, Modules, and Algebras

Abstract Epimorphic images of compact (algebraically compact) abelian groups are called cotorsion groups after Harrison. In a recent paper, Ph. Schultz raised the question whether “cotorsion” is a property which can be recognized by its small cotorsion epimorphic images: If G is a torsion-free group such that every torsion-free reduced homomorphic image of cardinality is cotorsion, is G necessarily cortorsion? In this note we will give some counterexamples to this problem. In fact, there is no cardinal k which is large enough to test cotorsion.