Unit Group of the Group Algebra $\mathbb{F}_qGL(2,7)$
Unit Group of the Group Algebra $\mathbb{F}_qGL(2,7)$
In this paper, we consider the general linear group $GL(2, 7)$ of $2 \times 2$ invertible matrices over the finite field of order $7$ and compute the unit group of the semisimple group algebra $\mathbb{F}_qGL(2,7)$, where $\mathbb{F}_q$ is a finite field. For the computation of the unit group, we need …