Christopher Herbig

collaborators

4 papers

math.RT2026

Character values and conductors of low-rank groups of Lie type

Christopher Herbig, Nguyen N. Hung

Let $I ¨ $ be a complex irreducible character of a finite group $G$ . The conductor of $I ¨ $ , denoted $c (I ¨ )$ , is the smallest positive integer $n$ such that $Ï(x)\in \mathbb{Q}(\exp(…

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 $I^\pm$ is a sum of $k$ complex roots of unity and $Q_{c (I^\pm)}$ is the smallest cyclotomic field containing $I^\pm$ ,…

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…

Character values and conductors of low-rank groups of Lie type

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