Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Subgroups of direct products of graphs of groups with free abelian
  vertex groups   A result of Baumslag and Roseblade states that a finitely presented subgroup
of the direct product of two free groups is virtually a direct product of free
groups. In this paper we generalise this result to the class of cyclic subgroup
separable graphs of groups with free abelian vertex groups and cyclic edge
groups. More precisely, we show that a finitely presented subgroup of the
direct product of two groups in this class is virtually $H$-by-(free abelian),
where $H$ is the direct product of two groups in the class. In particular, our
result applies to 2-dimensional coherent right-angled Artin groups and
residually finite tubular groups. Furthermore, we show that the multiple
conjugacy problem and the membership problem are decidable for finitely
presented subgroups of the direct product of two $2$-dimensional coherent
RAAGs.

20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: eess
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th