Expansion of conjugacy classes in \(\mathrm{PSL}_2(q)\). (Q889904)

For any conjugacy class \(\mathcal C\) in \(G=\mathrm{PSL}_2(q)\), the author computes \(\mathcal C^2\) and discusses whether or not \(C\) contains a triple of elements whose product is 1 which generates \(G\). This result extends for the group \(G\) a result of \textit{R. Guralnick} and \textit{G. Malle} [J. Am. Math. Soc. 25, No. 1, 77-121 (2012; Zbl 1286.20007)]. Moreover, the author determines which elements of \(G\) can be written as a product of two conjugate elements that generate \(G\).