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

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.