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Abelian groups with small cotorsion images

Part of: Abelian groups

Published online by Cambridge University Press:  09 April 2009

Rüdiger Göbel
Rüdiger Göbel
Affiliation:
Universität Essen GHS Universitätsstr. 3 D4300 Essen 1, Germany
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Abstract

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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.

MSC classification

Secondary: 20K30: Automorphisms, homomorphisms, endomorphisms, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 50 , Issue 2 , April 1991 , pp. 243 - 247
Copyright
Copyright © Australian Mathematical Society 1991

References

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