characterization of finite groups by the number of elements of prime order

Let s be a non-abelian simple group non-isomorphic to l2(q),where q is a mersenne prime and p be the greatest prime divisor of jsj. in[6, conjecture e] a. moreto conjectured that if every nite group g that isgenerated by elements of order p and has the same number of elements oforder p as s, then g=z(g)=s. in this paper, we verify the conjecture forthe sporadic simple groups.