Hostname: page-component-848d4c4894-mwx4w Total loading time: 0 Render date: 2024-07-01T04:51:34.942Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1]Corner, A. L. S. and Göbel, R., ‘Prescribing endomorphism algebras, a unified treatment’, Proc. London Math. Soc. (3) 50 (1985), 447–479.CrossRefGoogle Scholar
[2]Eklof, P. and Mekler, A., Almost free modules, set theoretic methods, (North-Holland, 1990).Google Scholar
[3]Fuchs, L., Infinite abelian groups, Vols. I, II, (Academic Press, New York, 1970, 1973).Google Scholar
[4]Göbel, R. and Shelah, S., ‘On semirigid classes of torsion-free abelian groups’, J. Algebra 93 (1985), 136–150.CrossRefGoogle Scholar
[5]Göbel, R., ‘On stout and slender groups’, J. Algebra 35 (1975), 39–55.CrossRefGoogle Scholar
[6]Göbel, R. and Wald, B., ‘Wachstumstypen und schlanke Gruppen’, Symposia Mathematica 23 (1979), 201–239.Google Scholar
[7]Hausen, J., ‘Automorphismengesättigte Klassen abzählbarer abelscher Gruppen’, Studies on Abelian Groups, pp. 146–181, (Springer-Verlag, Berlin 1968).Google Scholar
[8]Schultz, Ph., Self-splitting groups, (Report 23, 08 1988, University of Western Australia), to appear.Google Scholar