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