| Full text | |
| Author(s): |
Jespers, E.
[1]
;
Juriaans, S. O.
[2]
;
Kiefer, A.
[1]
;
de A e Silva, A.
[3]
;
Souza Filho, A. C.
[4]
Total Authors: 5
|
| Affiliation: | [1] Vrije Univ Brussel, Dept Math, B-1050 Brussels - Belgium
[2] Univ Sao Paulo, IME, BR-05315970 Sao Paulo - Brazil
[3] Univ Fed Paraiba, Ctr Ciencias Exatas & Nat, Dept Matemat, BR-58051900 Joao Pessoa, Paraiba - Brazil
[4] Univ Sao Paulo, EACH, BR-03828000 Sao Paulo - Brazil
Total Affiliations: 4
|
| Document type: | Journal article |
| Source: | Mathematics of Computation; v. 84, n. 293, p. 1489-1520, MAY 2015. |
| Web of Science Citations: | 5 |
| Abstract | |
We give an algorithm to determine finitely many generators for a subgroup of finite index in the unit group of an integral group ring ZG of a finite nilpotent group G, this provided the rational group algebra QG does not have simple components that are division classical quaternion algebras or two-by-two matrices over a classical quaternion algebra with center Q. The main difficulty is to deal with orders in quaternion algebras over the rationals or a quadratic imaginary extension of the rationals. In order to deal with these we give a finite and easy implementable algorithm to compute a polyhedron containing a fundamental domain in the hyperbolic three space H-3 (respectively, hyperbolic two space H-2) for a discrete subgroup of PSL2(C) (respectively, PSL2(R)) of finite covolume. Our results on group rings are a continuation of earlier work of Ritter and Sehgal, Jespers and Leal. (AU) | |
| FAPESP's process: | 11/11315-7 - Units in orders of finite dimensional algebras |
| Grantee: | Antonio Calixto de Souza Filho |
| Support Opportunities: | Regular Research Grants |