ON THE NUMBER OF THE IRREDUCIBLE CHARACTERS OF FACTOR GROUPS

Abstract. Let G be a finite group and let N be a normal subgroup of G. Suppose that Irr(GjN) is the set of the irreducible characters of G that contain N in their kernels. In this paper, we classify solvable groups G in which the set C(G) = fIrr(GjN)j1 6= N E Gg has at most three elements. We also compute the set C(G) for such groups.