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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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Keywords: Densely divisible, divisible, locally compact abelian, p-adic integers, p-adic numbers, Q-dense, quasicyclic, solenoidal
Article copyright: © Copyright 1972 American Mathematical Society

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