THE ACTION OF THE LINEAR CHARACTERGROUP ON THE SET OF NON-LINEARIRREDUCIBLE CHARACTERSTHE ACTION OF THE LINEAR CHARACTERGROUP ON THE SET OF NON-LINEARIRREDUCIBLE CHARACTERS

摘要

Let G be a nonabelian finite group. Then Irr(G/G’) is an abelian group under the multiplication of characters and acts on the set of non-linear irreducible characters of G via the multiplication of characters. The purpose of this paper is to establish some facts about the action of linear character group on non-linear irreducible characters and determine the structures of groups G for which either all the orbit kernels are trivial or the number of orbits is at most two. Using the established results on this action, it is very easy to classify groups G having at most three non-linear irreducible characters.