1 citations · 1 across the 5 of their papers we have counts for
6 papers
On a question of Navarro on the field of values of characters of solvable groups
Christopher Herbig
In a 2023 survey paper, Gabriel Navarro posed the following problem: Given an irreducible character of some solvable group where either is 2-rational or has odd degree,…
A Determination of -groups of Order
Christopher Herbig
A group is said to be a -group if whenever a primitive permutation group contains a regular subgroup isomorphic to , then is doubly transitive. Going as far back…
Character values and conductors of low-rank groups of Lie type
Christopher Herbig, Nguyen N. Hung
Let be a complex irreducible character of a finite group . The conductor of , denoted , is the smallest positive integer such that $χ(x)\in \mathbb{Q}(\exp({2πi…
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 takes values which may be expressed as sums of or fewer roots of unity. In this note, we prove a result which describes the irre…
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 is a sum of complex roots of unity and is the smallest cyclotomic field containing , is…
A Block-theoretic Proof of Burnside's Normal -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 -complement Theorem. Unfortunately, the proof contains an error. We take t…