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

 

On $ Q$-dense and densely divisible $ {\rm LCA}$ groups


Authors: D. L. Armacost and W. L. Armacost
Journal: Proc. Amer. Math. Soc. 36 (1972), 301-305
MSC: Primary 22B05
MathSciNet review: 0306401
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Abstract: In this note the structure of those LCA groups containing a dense subgroup isomorphic to the additive group of rational numbers is investigated. As a result of this investigation, it is shown that an LCA group containing a dense divisible subgroup of finite rank must be divisible.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0306401-7
PII: S 0002-9939(1972)0306401-7
Keywords: Densely divisible, divisible, locally compact abelian, p-adic integers, p-adic numbers, Q-dense, quasicyclic, solenoidal
Article copyright: © Copyright 1972 American Mathematical Society