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›› 2006, Vol. 23 ›› Issue (5): 597-600.DOI: 10.7523/j.issn.2095-6134.2006.5.005

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On the Structure of Augmentation Quotient Groups

ZHAO Hong-Mei, TANG Guo-Ping   

  1. 1.School of Science, Northwestern Polytechnical University, Xi’an, 710072, P.R.China


    2.Department of Mathematics, Graduate School of Chinese Academy
    of Sciences, Beijing, 100049, P.R.China

  • Received:1900-01-01 Revised:1900-01-01 Online:2006-09-15

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

CLC Number: