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

2025/11/03 by Christopher Herbig, Herbig, Christopher
Mathematics · #05C25 (Secondary) #20C15 #20K01 (Primary) 20B05 #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Group Theory (math.GR) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2511.01782

openalex publication_date 2025/11/03 · openalex created_date 2025/11/06 · openalex updated_date 2026/07/28

Abstract

A character of a finite group having degree n takes values which may be expressed as sums of n 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.

Citations

• On vanishing sums for roots of unity

Related

• Group elements whose character values are roots of unity
• Zeros and roots of unity in character tables
• A uniform upper bound for the character degree sums and Gelfand-Graev-like characters for finite simple groups
• Denseness results for zeros and roots of unity in character tables
• Character degree sums of finite groups