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.References
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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
- Received by editor(s): August 4, 2005
- Published electronically: June 30, 2006
- Communicated by: Jonathan I. Hall
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 41-45
- MSC (2000): Primary 20C15, 20D10, 20B20
- DOI: https://doi.org/10.1090/S0002-9939-06-08628-X
- MathSciNet review: 2280172