Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Groups of prime degree and the Bateman-Horn Conjecture   As a consequence of the classification of finite simple groups, the
classification of permutation groups of prime degree is complete, apart from
the question of when the natural degree $(q^n-1)/(q-1)$ of ${\rm PSL}_n(q)$ is
prime. We present heuristic arguments and computational evidence based on the
Bateman-Horn Conjecture to support a conjecture that for each prime $n\ge 3$
there are infinitely many primes of this form, even if one restricts to prime
values of $q$. Similar arguments and results apply to the parameters of the
simple groups ${\rm PSL}_n(q)$, ${\rm PSU}_n(q)$ and ${\rm PSp}_{2n}(q)$ which
arise in the work of Dixon and Zalesskii on linear groups of prime degree.

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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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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: dg-ga
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The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph