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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Dense pure subgroups of locally compact groups


Author: M. I. Kabenyuk
Journal: Proc. Amer. Math. Soc. 117 (1993), 537-539
MSC: Primary 22B05
MathSciNet review: 1145946
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Abstract: We prove that a locally compact abelian (LCA) group has no proper dense pure subgroups if and only if it does not have proper dense subgroups. This solves a problem of Armacost.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1145946-0
PII: S 0002-9939(1993)1145946-0
Keywords: Locally compact abelian groups, pure subgroups, nonclosed subgroups, dense subgroups, dense direct summands
Article copyright: © Copyright 1993 American Mathematical Society