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Dense pure subgroups of locally compact groups

Published:1993 Issue:2 Volume:117 Page:537-539
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Kabenyuk M. I.

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1993-117-02/S0002-9939-1993-1145946-0/S0002-9939-1993-1145946-0.pdf

Reference8 articles.

1. Monographs and Textbooks in Pure and Applied Mathematics;Armacost, David L.,1981

2. Dense decompositions of locally compact groups;Dietrich, William E., Jr.;Colloq. Math.,1971

3. Pure and Applied Mathematics, Vol. 36;Fuchs, László,1970

4. Dense subgroups of locally compact abelian groups;Kabenjuk, M. I.;Sibirsk. Mat. Zh.,1980

5. Chain conditions on subgroups of LCA groups;Khan, M. A.;Pacific J. Math.,1980

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