Unidades de ZC2p e Aplicações / Units of ZC2p and Applications
AUTOR(ES)
Renata Rodrigues Marcuz Silva
FONTE
IBICT - Instituto Brasileiro de Informação em Ciência e Tecnologia
DATA DE PUBLICAÇÃO
13/04/2012
RESUMO
Let p be an odd prime integer, be a pth primitive root of unity, Cn be the cyclic group of order n, and U(ZG) the units of the Integral Group Ring ZG: Consider ui := 1++2 +: : :+i1 for 2 i p + 1 2 : In our study we describe explicitly the generator set of U(ZC2p); where p is such that S := f1; ; u2; : : : ; up1 2 g generates U(Z[]) and U(Zp) is such that U(Zp) = 2 or U(Zp)2 = 2 and 1 =2 U(Zp)2; which occurs for p = 7; 11; 13; 19; 23; 29; 37; 53; 59; 61, and 67: For another values of p we don\ t know if such conditions hold. In addition, under suitable hypotheses, we extend these ideas and build a generator set of U(Z(C2p C2)) and U(Z(C2p C2 C2)): Besides that, using the previous results, we exhibit a generator set for the central units of the group ring Z(Cp Q8) where Q8 represents the quaternion group.
ASSUNTO(S)
cental units of integral group rings group rings over integers grupos dos quaternios quaternion group. unidades centrais de aneis de grupos unidades de aneis de grupo untis of group rings
