Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The pro-nilpotent group topology on a free group   In this paper, we work on the pro-nilpotent group topology of a free group.
First we investigate the closure of the product of finitely many subgroups of a
free group in the pro-nilpotent group topology. We present an algorithm for the
calculation of the closure in the pro-nilpotent group topology of the product
of finitely many finitely generated subgroups of a free group. Then we deduce
that the nil-closure of a rational subset is computable. We also prove that the
pseudovarieties V malcev G_nil, for every decidable pseudovariety of monoids V,
and J * G_nil are decidable.

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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph