Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite Groups that are the union of at most 25 proper subgroups   For a finite group $G$ let $\sigma(G)$ (the "sum" of $G$) be the least number
of proper subgroups of $G$ whose set-theoretical union is equal to $G$, and
$\sigma(G)=\infty$ if $G$ is cyclic. We say that a group $G$ is
$\sigma$-elementary if for every non-trivial normal subgroup $N$ of $G$ we have
$\sigma(G)<\sigma(G/N)$. In this paper we produce the list of all the
$\sigma$-elementary groups of sum up to 25. We also show that
$\sigma(\Aut(PSL(2,8)))=29$.

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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess