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Irreducible characters which are zero on only one conjugacy class
Author(s):
John
D.
Dixon;
A.
Rahnamai Barghi
Journal:
Proc. Amer. Math. Soc.
135
(2007),
41-45.
MSC (2000):
Primary 20C15, 20D10, 20B20
Posted:
June 30, 2006
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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.
References:
-
- 1.
- Ya. G. Berkovich and E.M. Zhmud', Characters of Finite Groups. Part (2), Vol. 181, Mathematical Monographs, Amer. Math. Soc., Rhode Island, 1999. MR 1650707 (99j:20007)
- 2.
- D. Chillag, On zeros of characters of finite groups, Proc. Amer. Math. Soc. 127 (1999) 977-983. MR 1487363 (99f:20012)
- 3.
- J.H. Conway et al., Atlas of Finite Simple Groups, Clarendon Press, Oxford, 1985. MR 0827219 (88g:20025)
- 4.
- The GAP Group, GAP-Groups, Algorithms and Programming, Version 4.4.4 (2005) (http://www.gap-system.org).
- 5.
- Ch. Hering, Transitive linear groups and linear groups which contain irreducible subgroups of prime order, Geometriae Dedicata 2 (1974) 425-460. MR 0335659 (49:439)
- 6.
- Ch. Hering, Transitive linear groups and linear groups which contain irreducible subgroups of prime order II, J. Algebra 93 (1985) 151-164. MR 0780488 (86k:20046)
- 7.
- B. Huppert, Endliche Gruppen I, Springer-Verlag, Berlin, 1967. MR 0224703 (37:302)
- 8.
- B. Huppert and N. Blackburn, Finite Groups III, Springer-Verlag, Berlin, 1982. MR 0662826 (84i:20001b)
- 9.
- I.M. Isaacs, Character Theory of Finite Groups, Academic Press, New York, 1976. MR 0460423 (57:417)
- 10.
- I.M. Isaacs, Character degrees and derived length of a solvable group, Canad. J. Math. 27 (1975) 146-151. MR 0357571 (50:10039)
- 11.
- E.M. Zhmud', On finite groups having an irreducible complex character with one class of zeros, Soviet Math. Dokl. 20 (1979) 795-797. MR 0553828 (81g:20020)
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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:
10.1090/S0002-9939-06-08628-X
PII:
S 0002-9939(06)08628-X
Received by editor(s):
August 4, 2005
Posted:
June 30, 2006
Communicated by:
Jonathan I. Hall
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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