Abstract
Finite groups with very few character values are characterized. The following is the main result of this article: A finite non-abelian group has precisely four character values if and only if it is the generalized dihedral group of a non-trivial elementary abelian 3-group. The proof involves the analysis of the centralizers of involutions.
2010 MATHEMATICS SUBJECT CLASSIFICATION:
Acknowledgments
The author would like to thank Shigeo Koshitani and Chris Parker for helpful comments. The author would also like to thank the anonymous referee for suggesting the more group-theoretic proof of Lemma 4.3(i).