Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Structure of group rings and the group of units of integral group rings:
  an invitation   During the past three decades fundamental progress has been made on
constructing large torsion-free subgroups (i.e. subgroups of finite index) of
the unit group $\U (\Z G)$ of the integral group ring $\Z G$ of a finite group
$G$. These constructions rely on explicit constructions of units in $\Z G$ and
proofs of main results make use of the description of the Wedderburn components
of the rational group algebra $\Q G$. The latter relies on explicit
constructions of primitive central idempotents and the rational representations
of $G$. It turns out that the existence of reduced two degree representations
play a crucial role. Although the unit group is far from being understood, some
structure results on this group have been obtained. In this paper we give a
survey of some of the fundamental results and the essential needed techniques.

24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th