English

On Generalized Characters Whose Values on Nonidentity Elements are Sums of at Most Two Roots of Unity

Group Theory 2025-11-06 v3

Abstract

A character of a finite group having degree nn takes values which may be expressed as sums of nn or fewer roots of unity. In this note, we prove a result which describes the irreducible constituents of generalized characters on abelian groups whose values on nonidentity elements are expressible as sums of two or fewer roots of unity. In Section 4, we apply our main result to obtain information about the connectivity of prime graphs for groups admitting such characters.

Keywords

Cite

@article{arxiv.2511.01782,
  title  = {On Generalized Characters Whose Values on Nonidentity Elements are Sums of at Most Two Roots of Unity},
  author = {Christopher Herbig},
  journal= {arXiv preprint arXiv:2511.01782},
  year   = {2025}
}