Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-25T23:53:36.651Z Has data issue: false hasContentIssue false
  • English
  • Français

Pure subgroups of LCA groups

Published online by Cambridge University Press:  17 April 2009

Sheng L. Wu
Sheng L. Wu
Affiliation:
Department of Mathematics, University of Oregon, Eugene OR 97403, United States of America
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.

This paper originated with our interest in the open question “If every pure subgroup of an LCA group G is closed, must G be discrete ?” that was raised by Armacost. The answer was surprisingly easy, but led to some interesting questions. We attempted to characterise those LCA groups that contain a proper pure dense subgroup, and found that every non-discrete torsion-free LCA group contains a proper pure dense subgroup; so does every non-discrete infinite self-dual torsion LCA group. We also give a necessary and sufficient condition for a torsion LCA group to contain a proper pure dense subgroup.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 47 , Issue 2 , April 1993 , pp. 199 - 204
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Armacost, D.L., The structure of locally compact abelian groups (Marcel Dekker Inc., New York, Basel, 1981).Google Scholar
[2]Comfort, W.W., ‘Recent topological developments on topological groups’, Proceedings of the 1992 Prague Topological Symposium (to appear).Google Scholar
[3]Fuch, L., Infinite Abelian groups (Academic Press, New York and London, 1970).Google Scholar
[4]Hewitt, E. and Ross, K.A., Abstract harmonic analysis I (Springer-Verlag, Berlin, Heidelberg, New York, 1979).CrossRefGoogle Scholar
[5]Wu, S.L., ‘Classification of self-dual torsion-free LCA Groups’, Fund. Math. 140 (1992).Google Scholar