Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Limit Points of Commuting Probabilities of Finite Groups   The commuting probability of a finite group $G$ is the probability that two
randomly chosen elements commute. Let $S\subseteq(0,1]$ denote the set of all
possible commuting probabilities of finite groups. We prove that $S\cup\{0\}$
is closed, which was conjectured by Keith Joseph in 1977.

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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: nlin