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

Year 2022, Volume: 32 Issue: 32, 176 - 191, 16.07.2022

Harish Chandra Shivangni Mıshra

https://doi.org/10.24330/ieja.1077623

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 $p>0$.

Keywords

Group algebras, unit groups, jacobson radical

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