Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Twisted conjugacy in $SL_n$ and $GL_n$ over subrings of $\bar{\mathbb
  F}_p(t)$   Let $\phi:G\to G$ be an automorphism of an infinite group $G$. One has an
equivalence relation $\sim_\phi$ on $G$ defined as $x\sim_\phi y$ if there
exists a $z\in G$ such that $y=zx\phi(z^{-1})$. The equivalence classes are
called $\phi$-twisted conjugacy classes and the set $G/\!\!\sim_\phi$ of
equivalence classes is denoted $\mathcal R(\phi)$. The cardinality $R(\phi)$ of
$\mathcal R(\phi)$ is called the Reidemeister number of $\phi$. We write
$R(\phi)=\infty$ when $\mathcal R(\phi)$ is infinite. We say that $G$ has the
$R_\infty$-{\it property} if $R(\phi)=\infty$ for every automorphism $\phi$ of
$G$. We show that the groups $G=GL_n(R), SL_n(R)$ have the $R_\infty$-property
for all $n\ge 3$ when $ F[t]\subset R\subsetneq F(t)$ where $F$ is a subfield
of $\bar{\mathbb F}_p$. When $n\ge 4$, we show that any subgroup $H\subset
GL_n(R)$ that contains $SL_n(R)$ also has the $R_\infty$-property.

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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin