Remarks on the generation of orthogonal groups over finite fields (Q1902146)

The authors show: Let \(O(V)\) be the orthogonal group of a nonsingular quadratic space of dimension \(n\) over a finite field \(K\). Then \(O(V)\) is generated by two elements. In addition, if \(\text{char }K=2\) and \(|K|\neq 2\), then \(O(V)\) is generated by \(n+1\) symmetries. The present paper deals mainly with the cases \(\text{char }K=2\) and \(|K|=3\) and relies for the other cases on results by \textit{H. Ishibashi} and \textit{A. G. Earnest} [in J. Algebra 165, 164-171 (1994; Zbl 0805.20039)].