ON THOMPSONS CONJECTURE

Lee G be a finite group and N(G) = {n is an element of N\G has a conju gacy class C, such that \C\ = n}. Professor J. G. Thompson has conject ured that ''If G be a finite group with Z(G) = 1 and M a nonabelian si mple group satisfying that N(G) = N(M), then G congruent to M.'' We ha ve proved that if M is a sporadic simple group, then Thompson's conjec ture is correct. In this paper, we shall further prove that if M is a finite simple group having at least three prime graph components, then the conjecture is also correct. (C) 1996 Academic Press, Inc.