关键词: 整数环, 增广商群, 二面体群

Abstract: Let G be a finite group, ZG its integral group ring and
n(G) the nth power
of the augmentation ideal
(G), denote Qn(G) =
n(G)/
n+1(G) the augmentation
quotient groups of G. In this paper we give a set of generators for
n(G) related to the
Sylow p−subgroup of G. At last the structure of Qn(D2tk) for dihedral group D2tk is
discussed and Qn(D2tk) ∼= Qn(D2t ) is proved.

Key words: integral group ring, augmentation quotient group, dihedral group