| Reference : From the Poincaré theorem to generators of the unit group of integral group rings of ... |
| Scientific journals : Article | |||
| Physical, chemical, mathematical & earth Sciences : Mathematics | |||
| http://hdl.handle.net/10993/45741 | |||
| From the Poincaré theorem to generators of the unit group of integral group rings of finite groups | |
| English | |
Jespers, E.  [> >] | |
| Juriaans, S. O. [> >] | |
| Kiefer, Ann [University of Luxembourg > Faculty of Humanities, Education and Social Sciences (FHSE) > LUCET] | |
| de A. e Silva, A. [> >] | |
| Souza Filho, A. C. [> >] | |
| 2015 | |
| Math. Comp. | |
| 84 | |
| 293 | |
| 1489--1520 | |
| Yes | |
| [en] Units ; Group Rings ; Fundamental Domain ; Generator | |
| [en] 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 centre 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 fundamental domain in the hyperbolic three space H 3 (respectively hyperbolic two space H 2 ) for a discrete subgroup of PSL 2 (C) (respectively PSL 2 (R)) of finite covolume. Our results on group rings are a continuation of earlier work of Ritter and Sehgal, Jespers and Leal. | |
| http://hdl.handle.net/10993/45741 | |
| 10.1090/S0025-5718-2014-02865-2 | |
| http://dx.doi.org/10.1090/S0025-5718-2014-02865-2 |
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