On the growth sequences of PSp(2m,q)

Abstract

The aim of this paper is to give a lower bound for h(2,PSp(2m,q)), for all 2 ≤ m ≤ 5, m ≥ 10 and q ≥ 2, where h(2,G) is the maximum number such that G h(2,G) can be generated by 2 elements. Furthermore, we consider a problem which was conjectured by J.Wiegold and the first author in 1996, which says that h(2,G) 2 > |G| for all finite non-abelian simple groups. We confirm the conjecture for the projective symplectic simple groups PSp(2m,q) at the end.