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 $Sp_{ 2n}(q)$ are $(2,3)$-generated for all $n\geq 4$. Because of the existing literature, this result implies that the groups $PSp_{ 2n}(q)$ are $(2,3)$-generated for all $n\geq 2$, with the exception of $PSp_4(2^f)$ and $PSp_4(3^f)$.
Categories: math.GR