Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The $R_{\infty} property for abelian groups   It is well known there is no finitely generated abelian group which has the
$R_\infty$ property. We will show that also many non-finitely generated abelian
groups do not have the $R_\infty$ property, but this does not hold for all of
them. In fact we construct an uncountable number of infinite countable abelian
groups which do have the $R_{\infty}$ property. We also construct an abelian
group such that the cardinality of the Reidemeister classes is uncountable for
any automorphism of that group. 8 pages, no figures

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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: cs
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The categories of this paper are: cond-mat