Finite groups with very few character values
Group Theory
2021-03-16 v3 Representation Theory
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 -group. The proof involves the analysis of the centralizers of involutions.
Cite
@article{arxiv.2002.05742,
title = {Finite groups with very few character values},
author = {Taro Sakurai},
journal= {arXiv preprint arXiv:2002.05742},
year = {2021}
}
Comments
v1: 5 pages. Comments are welcome. v2: Proofs are improved. v3: Proofs are slightly more simplified