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 Sp2n(q) are (2,3)-generated for all n≥4. Because of the existing literature, this result implies that the groups PSp2n(q) are (2,3)-generated for all n≥2, with the exception of PSp4(2f) and PSp4(3f).