Mark L. Lewis

collaborators

6 papers

math.GR2026

On a theorem of Artin and the dimension of the space spanned by the rational valued characters of a group

Mark L. Lewis

In this paper, we sharpen a theorem of Artin to show that for a finite group, the dimension of the subspace of class functions spanned by the rational valued characters equals the…

math.GR2025

Kernels of Brauer characters and Isaacs' partial characters

Mark L. Lewis

In this paper, we prove a property of kernels of Brauer characters. We propose a candidate for the kernels of Isaacs' partial characters, and we show that this candidate has the sa…

math.GR2025

Isaacs' Generalization of Taketa's theorem

Xiaoyou Chen, Mark L. Lewis

We generalize the definition of pseudo monomial characters and $M$ -groups to the Brauer character and Isaacs' $I ¨ $ -partial character settings. We prove an analogs of Isaacs's gener…

math.GR2025

A converse for a theorem of Gallagher

Xiaoyou Chen, Mark L. Lewis

Let $G$ be a finite group. Suppose $N$ is a normal subgroup of $G$ . Recall that Gallagher's theorem states that if $I ¨ \in Irr (G)$ satisfies $I ¨ _{N}$ is irreducible, then $ÏÎ²…

math.GR2025

On Camina pairs and the Fitting subgroup

Mark L. Lewis, Emanuele Pacifici

In this paper, we consider the relationship between the Fitting subgroup and the Camina kernel of a Camina pair.

math.CO2025

On the Number of Disconnected Character Degree Graphs Satisfying PÃ¡lfy's Inequality

Mark L. Lewis, Andrew Summers

Let $G$ be a finite solvable group with disconnected character degree graph $I^ (G)$ . Under these conditions, it follows from a result of PÃ¡lfy that $I^ (G)$ consists of two connect…