Czechoslovak Mathematical Journal, first online, pp. 1-3


Groups with only two nonlinear non-faithful irreducible characters

Xiaoyou Chen, Mark L. Lewis

Received July 26, 2017.   First published December 14, 2017.

Abstract:  We determine the groups with exactly two nonlinear non-faithful irreducible characters whose kernels intersect trivially.
Keywords:  non-faithful character; nonlinear character; finite group
Classification MSC:  20C15
DOI:  10.21136/CMJ.2017.0348-17

PDF available at:  Springer   Institute of Mathematics CAS

References:
[1] A. Iranmanesh, A. Saeidi: Finite groups with a unique nonlinear nonfaithful irreducible character. Arch. Math., Brno 47 (2011), 91-98. MR 2813535 | Zbl 1249.20009
[2] Y. Li, X. Chen, H. Li: Finite $p$-groups with exactly two nonlinear non-faithful irreducible characters. To appear in Czech. Math. J.
[3] A. Saeidi: Classification of solvable groups possessing a unique nonlinear non-faithful irreducible character. Cent. Eur. J. Math. 12 (2014), 79-83. DOI 10.2478/s11533-013-0327-4 | MR 3121823 | Zbl 1287.20013
[4] G. Seitz: Finite groups having only one irreducible representation of degree greater than one. Proc. Am. Math. Soc. 19 (1968), 459-461. DOI 10.1090/S0002-9939-1968-0222160-X | MR 0222160 | Zbl 0244.20010
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Affiliations:   Xiaoyou Chen, College of Science, Henan University of Technology, No. 100 Lianhua Road, Zhengzhou 450001, Henan, China, e-mail: cxymathematics@hotmail.com; Mark L. Lewis, Department of Mathematical Sciences, Kent State University, 233 MSB, 1300 Lefton Esplanade, P. O. Box 5190, Kent 44242-0001, Ohio, USA, e-mail: lewis@math.kent.edu


 
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