Free groups in quaternion algebras

Autor(es)

Juriaans, S. O. ^[1] ; Souza Filho, A. C. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo IME USP, Inst Matemat & Estat, BR-05315970 Sao Paulo - Brazil

^[2] Univ Sao Paulo EACH USP, Escola Artes Ciencias & Humanidades, BR-03828000 Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Algebra; v. 379, p. 314-321, APR 1 2013.
• Citações Web of Science: 2

Resumo

In Juriaans et al. (2009) {[}9] we constructed pairs of units u, v in Z-orders of a quaternion algebra over Q(root-d), d a positive and square free integer with d equivalent to 7 (mod 8), such that (u(n), v(n)) is free for some n is an element of N. Here we extend this result to any imaginary quadratic extension of Q, thus including matrix algebras. More precisely, we show that < u(n), v(n)> is a free group for all n >= 1 and d > 2 and for d = 2 and all n >= 2. The units we use arise from Pell's and Gauss' equations. (C) 2013 Elsevier Inc. All rights reserved. (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