English

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 33-group. The proof involves the analysis of the centralizers of involutions.

Keywords

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

R2 v1 2026-06-23T13:41:19.445Z