Units of ZCp^n / Unidades de ZCpn
AUTOR(ES)
Patricia Massae Kitani
FONTE
IBICT - Instituto Brasileiro de Informação em Ciência e Tecnologia
DATA DE PUBLICAÇÃO
02/03/2012
RESUMO
Let Cp be a cyclic group of order p, where p is a prime integer such that S = {1, , 1 + \\theta, 1 +\\theta +\\theta ^2 , · · · , 1 + \\theta + · · · +\\theta ^{p-3/2}} generates the group of units of Z[\\theta] and is a primitive pth root of 1 over Q. In the article \"Units of ZCp\" , Ferraz gave an easy way to nd a set of multiplicatively independent generators of the group of units of the integral group ring ZCp . We extended this result for ZCp^n , provided that a set similar to S generates the group of units of Z[\\theta]. This occurs, for example, when \\phi(p^n)\\leq 66. We described the group of units of ZCp^n as the product ±ker(\\pi_1) × Im(\\pi_1), where \\pi_1 is a group homomorphism. Moreover, we explicited a basis of ker(\\pi_1) and I m(\\pi_1).
ASSUNTO(S)
normalized symmetric units and cyclotomic units. anéis de grupo cyclic groups group rings grupos cíclicos unidades de anéis de grupo sobre os inteiros unidades simétricas normalizadas e unidades ciclotômicas. units of integral group rings
