Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalization of order separability for free products and omnipotence
  of free products of groups   It was proved that for any finite set of elements of a free product of
residually finite groups such that no two of them belong to conjugate cyclic
subgroups and each of them do not belong to a subgroup which is conjugate a to
free factor there exists a homomorphism of the free product onto a finite group
such that the order of the image of each fixed element is an arbitrary multiple
of a constant number.

1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con