Unit groups of group algebras of non abelian group of order up to 30

Abstract

In this paper, we characterize the structure of unit group of semisimple group algebra $F_{q}G$, where $G$ is non abelian group of order up to 30 and $F_{q}$ is a field of order $q(=p^{k})$, p is a prime number. In particular, we have characterized the structure of unit group of group algebra of 7 non abelian groups of order 16, $C_{7}\rtimes C_{3}$ of order 21, $C_{9}\rtimes C_{3}$ of order 27, $C_{7}\rtimes C_{4}$ of order 28 and $C_{5}\times S_{3}$ of order 30. Unit groups of semisimple group algebras for non abelian groups up to order 30 have now been thoroughly studied.