Irreducible characters which are zero on only one conjugacy class

Dixon, John; Rahnamai Barghi, A.

doi:10.1090/S0002-9939-06-08628-X

Irreducible characters which are zero on only one conjugacy class
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by John D. Dixon and A. Rahnamai Barghi PDF

Proc. Amer. Math. Soc. 135 (2007), 41-45 Request permission

Abstract:

Suppose that $G$ is a finite solvable group which has an irreducible character $\chi$ which 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 classified by Huppert. We can also say more about the structure of $G$ depending on whether $\chi$ is primitive or not.

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