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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
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Abstract

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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

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