The group of units of group algebras of abelian groups of order 36 and $C_{3}\times A_{4}$ over any finite field

Abstract

Let $\mathcal{FG}$ be the group algebra of the group $\mathcal{G}$ over the field $\mathcal{F}$ having characteristic $p>0$ and $q=p^{n}$ elements and $\mathscr{U}\mathcal{(FG)}$ be the unit group of $\mathcal{FG}$. In this paper, we are proceeding to determine the structure of unit group of group algebra of all four non isomorphic abelian groups and one non abelian group $C_{3}\times A_{4}$ of order $36$, for any prime $p>0$.