Irreducible characters which are zero on only one conjugacy class

Abstract

Suppose that G is a …nite solvable group which has an irreducible characterwhich vanishes on exactly one conjugacy class. Then we show that G has a homomorphic image which is a nontrivial 2-transitive permutation group. The latter groups have been classi…ed by Huppert. We can also say more about the structure of G depending on whether � is primitive or not. Mathematics Subject Classi…cation 2000: 20C15 20D10 20B20