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Czechoslovak Mathematical Journal

, Volume 64, Issue 1, pp 149–157 | Cite as

Unit groups of group algebras of some small groups

  • Gaohua Tang
  • Yangjiang Wei
  • Yuanlin Li
Article
  • 146 Downloads

Abstract

Let FG be a group algebra of a group G over a field F and U (FG) the unit group of FG. It is a classical question to determine the structure of the unit group of the group algebra of a finite group over a finite field. In this article, the structure of the unit group of the group algebra of the non-abelian group G with order 21 over any finite field of characteristic 3 is established. We also characterize the structure of the unit group of FA 4 over any finite field of characteristic 3 and the structure of the unit group of FQ 12 over any finite field of characteristic 2, where Q 12 = 〈x, y; x 6 = 1, y 2 = x 3, x y = x −1〉.

Keywords

group ring unit group augmentation ideal Jacobson radical 

MSC 2010

16S34 16U60 20C05 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2014

Authors and Affiliations

  1. 1.School of Mathematical ScienceGuangxi Teachers Education UniversityNanning, GuangxiP.R.China
  2. 2.Department of MathematicsBrock UniversitySt.CatharinesCanada

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