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 takes values which may be expressed as sums of 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}
}