Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on doubles of groups   Recently, Rips produced an example of a double of two free groups which has
unsolvable generalized word problem. In this paper, we show that Rips's example
fits into a large class of doubles of groups, each member of which contains F_2
x F_2 and therefore has unsolvable generalized word problem and is incoherent.

26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat