On the (2,3)-generation of the finite symplectic groups

Abstract

This paper is a new important step towards the complete classification of the finite simple groups which are $(2,3)$-generated. In fact, we prove that the symplectic groups $S{p}_{2n}(q)$ are $(2,3)$-generated for all $n\ge 4$. Because of the existing literature, this result implies that the groups $PS{p}_{2n}(q)$ are $(2,3)$-generated for all $n\ge 2$, with the exception of $PS{p}_4(2^f)$ and $PS{p}_4(3^f)$.