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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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: 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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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
PII: S 0002-9939(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.