On the Structure of Augmentation Quotient Groups

ZHAO Hong-Mei; TANG Guo-Ping

doi:10.7523/j.issn.2095-6134.2006.5.005

Journal of University of Chinese Academy of Sciences >

2006 , Vol. 23 >Issue 5: 597 - 600

DOI: https://doi.org/10.7523/j.issn.2095-6134.2006.5.005

论文

On the Structure of Augmentation Quotient Groups

ZHAO Hong-Mei ,
TANG Guo-Ping

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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 date: 1900-01-01

Revised date: 1900-01-01

Online published: 2006-09-15

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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

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ZHAO Hong-Mei , TANG Guo-Ping . On the Structure of Augmentation Quotient Groups[J]. Journal of University of Chinese Academy of Sciences, 2006 , 23(5) : 597 -600 . DOI: 10.7523/j.issn.2095-6134.2006.5.005

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