FROM THE POINCARE THEOREM TO GENERATORS OF THE UNIT GROUP OF INTEGRAL GROUP RINGS OF FINITE GROUPS

Autor(es)

Jespers, E. ^[1] ; Juriaans, S. O. ^[2] ; Kiefer, A. ^[1] ; de A e Silva, A. ^[3] ; Souza Filho, A. C. ^[4]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: Mathematics of Computation; v. 84, n. 293, p. 1489-1520, MAY 2015.
• Citações Web of Science: 5

Resumo

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)

• Processo FAPESP: 08/57930-1 - Unidades em ordens de algebras com aplicacoes em aneis de grupo, aneis de semi-grupos e teoria dos codigos
• Beneficiário: Antonio Calixto de Souza Filho
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 11/11315-7 - Unidades em ordens de álgebras de dimensão finita
• Beneficiário: Antonio Calixto de Souza Filho
• Modalidade de apoio: Auxílio à Pesquisa - Regular