On the unit group of a semisimple group algebra $\mathbb{F}_qSL(2, \mathbb{Z}_5)$

Abstract

We give the characterization of the unit group of $\mathbb{F}_qSL(2, \mathbb{Z}_5)$, where $\mathbb{F}_q$ is a finite field with $q = p^k$ elements for prime $p > 5,$ and $SL(2, \mathbb{Z}_5)$ denotes the special linear group of $2 \times2$ matrices having determinant $1$ over the cyclic group $\mathbb{Z}_5$.

Keywords

• unit group
• finite field
• wedderburn decomposition