Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On $2$-closed abelian permutation groups   A permutation group $G\le\operatorname{Sym}(\Omega)$ is said to be $2$-closed
if no group $H$ such that $G<H\le\operatorname{Sym}(\Omega)$ has the same
orbits on $\Omega\times\Omega$ as $G$. A simple and efficient inductive
criterion for the $2$-closedness is established for abelian permutation groups
with cyclic transitive constituents.

15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol