ABSTRACT Let G be a finite non-abelian simple group and d(G) the minimum number of generators of G. Then, h(2,G) is the maximum number n such that d(Gn) = 2, where Gn is the external direct products of n copies of G. The aim of this paper is to give a lower bound for h(2, PSL(m,q)), for all m = 2 and q = 2. Furthermore, we consider a problem which was conjectured by J. Wiegold and the author in 1996, which says that h(2, G)� > |G| for all finite non-abelian simple groups. Finally, we confirm the conjecture for the group PSL(m, q).

Keywords