Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Direct products and elementary equivalence of polycyclic-by-finite
  groups   We give an algebraic characterization of elementary equivalence for
polycyclic-by-finite groups. Using this characterization, we investigate the
relations between their elementary equivalence and the elementary equivalence
of the factors in their decompositions in direct products of indecomposable
groups. In particular we prove that the elementary equivalence of two such
groups G,H is equivalent to each of the following properties:
  1)Gx...xG (k times G) and Hx...xG (k times H) are elementarily equivalent for
a strictly positive integer k;
  2)AxG and AxH are elementarily equivalent for two elementarily equivalent
polycyclic-by-finite groups A,B.
  It is not presently known if 1) implies elementary equivalence for any groups
G,H.

34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat