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 is generated by elements of order p and has the same number of elements of order p as S, then G=Z(G) = S. In this paper, we verify the conjecture for the sporadic simple groups.