The unit group of group algebra $\mathbb{F}_qSL(2;\mathbb{Z}_3)$

Abstract

Let \(\mathbb{F}_q\) be a finite field of characteristic \(p\) having \(q\) elements, where \(q = p^k\) and \(p \ge 5\). Let \(SL(2,\mathbb{Z}_3)\) be the special linear group of \(2 \times 2\) matrices with determinant \(1\) over \(\mathbb{Z}_3\). In this note we establish the structure of the unit group of \(\mathbb{F}_qSL(2,\mathbb{Z}_3)\).

Received: 5 August 2015 | Accepted: 20 October 2015