Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On stability of asymptotic property C for products and some group
  extensions   We show that Dranishnikov's asymptotic property C is preserved by direct
products and the free product of discrete metric spaces. In particular, if $G$
and $H$ are groups with asymptotic property C, then both $G \times H$ and $G *
H$ have asymptotic property C. We also prove that a group~$G$ has asymptotic
property C if $1\to K\to G\to H\to 1$ is exact, if $\operatorname{asdim}
K<\infty$, and if $H$ has asymptotic property C. The groups are assumed to have
left-invariant proper metrics and need not be finitely generated. These results
settle questions of Dydak and Virk, of Bell and Moran, and an open problem in
topology from the Lviv Topological Seminar.

15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas