Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Crossed Product of Cyclic Groups   All crossed products of two cyclic groups are explicitly described using
generators and relations. A necessary and sufficient condition for an extension
of a group by a group to be a cyclic group is given.

30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph