Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Representing and counting the subgroups of the group Z_m x Z_n   We deduce a simple representation and the invariant factor decompositions of
the subgroups of the group $\Bbb{Z}_m \times \Bbb{Z}_n$, where $m$ and $n$ are
arbitrary positive integers. We obtain formulas for the total number of
subgroups and the number of subgroups of a given order.

10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess