Unit Group of the Group Algebra $\mathbb{F}_qGL(2,7)$
Namatchivayam Umapathy Sivaranjani,
Elumalai Nandakumar,
Gaurav Mittal
et al.
Abstract: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 the Wedderburn decomposition of $\mathbb{F}_qGL(2,7)$, which is determined by first computing the Wedderburn decomposition of the group algebra $\mathbb{F}_q(PSL(3, 2)\rtimes C_2)$. Here $PSL(3,2)$ is the project… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.