PRODUCTS OF CONJUGACY CLASSES IN SIMPLE GROUPS

Let G be a finite group. For a is an element of G, let a(G) = {a(g) vertical bar g is an element of G} be the conjugacy class of a in G. In this paper, we study a conjecture due to Arad and Herzog which asserts that in a finite non-abelian simple group the product of two nontrivial conjugacy classes is never a single conjugacy class. In particular, we will verify this conjecture for several families of finite simple groups of Lie type.