Article (Scientific journals)
From the Poincaré theorem to generators of the unit group of integral group rings of finite groups
Jespers, E.; Juriaans, S. O.; Kiefer, Ann et al.
2015In Mathematics of Computation, 84 (293), p. 1489--1520
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Keywords :
Units; Group Rings; Fundamental Domain; Generator
Abstract :
[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.
Disciplines :
Mathematics
Author, co-author :
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.
External co-authors :
yes
Language :
English
Title :
From the Poincaré theorem to generators of the unit group of integral group rings of finite groups
Publication date :
2015
Journal title :
Mathematics of Computation
ISSN :
1088-6842
Publisher :
American Mathematical Society, United States
Volume :
84
Issue :
293
Pages :
1489--1520
Peer reviewed :
Peer Reviewed verified by ORBi
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since 21 January 2021

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