Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A characterization of finitely generated reflection subgroups of Coxeter
  groups orthogonal to a reflection   Given a reflection $r$ in a Coxeter group $W$ (possibly of infinite rank), we
consider the subgroup of $W$ generated by the reflections in $W$ having
(-1)-eigenvectors orthogonal to the (-1)-eigenvector of $r$. In this paper, we
determine completely when this subgroup is finitely generated, by using
preceding results on centralizers of reflections. This result provides a new
and naturally constructed example of a family of non-finitely generated
subgroups of finitely generated groups.

23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn