Christopher Herbig

collaborators

3 papers

math.GR2025

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

Christopher Herbig

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 irre…

math.NT2025

Answer to a Question of Hung and Tiep on Conductors of Cyclotomic Integers

Christopher Herbig

In Question 5.2 of [5], Hung and Tiep asked the following: If $α$ is a sum of $k$ complex roots of unity and $Q_{c (α)}$ is the smallest cyclotomic field containing $α$ , is…

math.GR2025

A Block-theoretic Proof of Burnside's Normal $p$ -complement Theorem

Christopher Herbig

In [3, Theorem 6.7B], the authors use the Main Theorems of Brauer to give a proof of Burnside's Normal $p$ -complement Theorem. Unfortunately, the proof contains an error. We take t…

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

Answer to a Question of Hung and Tiep on Conductors of Cyclotomic Integers

A Block-theoretic Proof of Burnside's Normal p-complement Theorem

A Block-theoretic Proof of Burnside's Normal $p$ -complement Theorem