Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: The virtual first Betti number of soluble groups
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th