Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On products of Groups with abelian subgroups of small index   It is proved that every group of the form $G=AB$ with two subgroups $A$ and
$B$ each of which is either abelian or has a quasicyclic subgroup of index $2$
is soluble of derived length at most $3$. In particular, if $A$ is abelian and
$B$ is a locally quaternion group, this gives a positive answer to Question
18.95 of "Kourovka notebook" posed by A.I.Sozutov.

30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex