On Products of Irreducible Characters and Products of Conjugacy Classes in Finite Groups

Let G a finite group. For conjugacy classes A and B of G, the subset AB of G is a union of conjugacy classes of G, and for irreducible complex characters χ and ϕ of G, the product χϕ is a linear combination of irreducible characters of G with positive integer coefficients. In this article we give the structure of finite groups G whenever C 2 contains a central conjugacy class or does not contain a central conjugacy class of G, for all conjugacy classes C of G. Also in the case of (C −1) m C n ⊆ Z(G) the structure of G is given. Similar results when C is replaced by an irreducible character χ of G are discussed.