# The unit group of group algebra $F_qSL(2;Z_3)$

Keywords:
Group algebra, Unit group, Finite field

### Abstract

Let $\F_q$ be a finite field of characteristic $p$ having $q$ elements, where $q = p^k$ and $p\ge 5$. Let $ SL(2,\Z_3)$ be the special linear group of $2\times2$ matrices with determinant $1$ over $\Z_3$. In this note we establish the structure of the unit group of $\F_q SL(2,\Z_3)$.