Irreducible characters which are zero on only one conjugacy class

Authors:
John D. Dixon and A. Rahnamai Barghi

Journal:
Proc. Amer. Math. Soc. **135** (2007), 41-45

MSC (2000):
Primary 20C15, 20D10, 20B20

Published electronically:
June 30, 2006

MathSciNet review:
2280172

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Abstract | References | Similar Articles | Additional Information

Abstract: Suppose that is a finite solvable group which has an irreducible character which vanishes on exactly one conjugacy class. Then we show that has a homomorphic image which is a nontrivial -transitive permutation group. The latter groups have been classified by Huppert. We can also say more about the structure of depending on whether is primitive or not.

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Additional Information

**John D. Dixon**

Affiliation:
School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6

**A. Rahnamai Barghi**

Affiliation:
Institute for Advanced Studies in Basic Sciences, Zanjan, P.O. Box 45195-1159, Iran – and – Islamic Azad University, Zanjan, P.O. Box 49195-467, Iran

Email:
rahnama@iasbs.ac.ir

DOI:
http://dx.doi.org/10.1090/S0002-9939-06-08628-X

Received by editor(s):
August 4, 2005

Published electronically:
June 30, 2006

Communicated by:
Jonathan I. Hall

Article copyright:
© Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.