The covering number of the group \(\text{PSL}_ n(F)\) (Q1920000)

Let \(G\) be a group, \(C\) a conjugacy class of \(G\) and \(C^k=\{c_1c_2\cdots c_k\mid c_i\in C\}\). The covering number \(cn(G)\) is the minimal value \(k\) such that \(C^k=G\) for every nontrivial conjugacy class \(C\) of \(G\). The author shows the following theorem. Let \(F\) be any field and let \(G\) be the projective special linear group \(\text{PSL}_n(F)\), where \(n\geq 3\) and \(|F|\geq 4\). If \(n=3\), assume in addition that either \(F\) is finite or algebraically closed. Then \(\text{cn}(G)=n\).