Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Limit points in the range of the commuting probability function on
  finite groups   If G is a finite group, then Pr(G) denotes the fraction of ordered pairs of
elements of G which commute. We show that, if l \in (2/9,1] is a limit point of
the function Pr on finite groups, then l \in \Q and there exists an e = e_l > 0
such that Pr(G) \not\in (l - e_l, l) for any finite group G. These results lend
support to some old conjectures of Keith Joseph.

15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin