J Austral Math Soc Ser A 50 pp243--247, 1991.

Abelian Groups with Small Cotorsion Images

Rüdiger Göbel

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 2^À₀ is cotorsion, is G necessarily cotorsion? 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.

1980 AMS Subject Classification (1985 Revision): 20K30

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Authors

Rüdiger Göbel

UNiversität Essen GHS, Universitätsstr. 3, D4300 Essen 1, Germany.