Let Fq be a finite field of characteristic p having q elements, where q = p and p ≥ 5. Let SL(2,Z3) be the special linear group of 2 × 2 matrices with determinant 1 over Z3. In this note we establish the structure of the unit group of FqSL(2,Z3). 2010 MSC: 16U60, 20C05
