Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The $p$-Zassenhaus Filtration of a Free Profinite Group and Shuffle
  Relations   For a prime number $p$ and a free profinite group $S$ on the basis $X$, let
$S_{(n,p)}$, $n=1,2,\ldots,$ be the $p$-Zassenhaus filtration of $S$. For
$p>n$, we give a word-combinatorial description of the cohomology group
$H^2(S/S_{(n,p)},\mathbb{Z}/p)$ in terms of the shuffle algebra on $X$. We give
a natural linear basis for this cohomology group, which is constructed by means
of unitriangular representations arising from Lyndon words.

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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph