Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conjugacy classes of centralizers in the group of upper triangular
  matrices   Let G be a group. Two elements x and y in G are said to be in the same
z-class if their centralizers in G are conjugate within G. In this paper, we
prove that the number of z-classes in the group of upper triangular matrices is
infinite provided that the field is infinite and size of the matrices is at
least 6, and finite otherwise.

23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys