Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Varietal Capability of Infinite Direct Products of Groups   Recently, the authors gave some conditions under which a direct product of
finitely many groups is $\mathcal{V}-$capable if and only if each of its
factors is $\mathcal{V}-$capable for some varieties $\mathcal{V}$. In this
paper, we extend this fact to any infinite direct product of groups. Moreover,
we conclude some results for $\mathcal{V}-$capability of direct products of
infinitely many groups in varieties of abelian, nilpotent and polynilpotent
groups.

30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess