Czechoslovak Mathematical Journal

, Volume 64, Issue 1, pp 149–157

# Unit groups of group algebras of some small groups

• Gaohua Tang
• Yangjiang Wei
• Yuanlin Li
Article

## 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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