On Thompsonʹs Conjecture Original Research Article

LetGbe a finite group andN(G)={nset membership, variantNGhas a conjugacy classC, such that C=n}. Professor J. G. Thompson has conjectured that “IfGbe a finite group withZ(G)=1 andMa nonabelian simple group satisfying thatN(G)=N(M), thenGcongruent withM.” We have proved that ifMis a sporadic simple group, then Thompsonʹs conjecture is correct. In this paper, we shall further prove that ifMis a finite simple group having at least three prime graph components, then the conjecture is also correct.