M. Lewis

activity

20242026

collaborators

17 papers

math.GR2026

Groups with a Fixed Character Degree: The General Case

Mark Lewis, Brandon Martin

We obtain arithmetic conditions which are satisfied by solvable groups admitting an abelian $π$ -subgroup. First, we extend a previous characterization by removing the square-free h…

math.GR2026

The category of centralizer lattices of groups

William Cocke, Mark L. Lewis, Ryan McCulloch

We formalize the concept of a centralizer-respecting homomorphism, surjective homomorphisms which are equivariant with respect to taking the centralizer of a subgroup. There is a f…

math.GR2026

Groups with a conjugacy class that is the difference of two normal subgroups

Mark L. Lewis, Lucia Morotti, Emanuele Pacifici +2

We consider finite groups having a conjugacy class that is the difference of two normal subgroups. That is, suppose $G$ is a group and $M$ and $N$ are normal subgroups so that $N <…

math.GR2025

Sylow subgroups and the number of irreducible characters of degrees divisible by a prime $p$

James P. Cossey, Mark L. Lewis, A. A. Schaeffer Fry +1

Let $G$ be a finite group and $p$ a prime. We establish an upper bound for the derived length of a Sylow $p$ -subgroup of $G$ in terms of the number of irreducible characters of $G$ …

math.GR2025

Groups Having a Character of Maximal Degree

Sara Jensen, Mark L. Lewis

Let $G$ be a group, let $d$ be a character degree, and let $e$ be the integer so that $∣ G ∣ = d (d + e)$ . It has been shown when $e > 1$ that $∣ G ∣ \leq e^{4} - e^{3}$ . In this paper, we con…

math.GR2025

Group cosets with all elements of equal order

Alan R. Camina, Rachel D. Camina, Mark L. Lewis +3

Let $G$ be a finite group and $N$ a proper, nontrivial, normal subgroup of $G$ . If, for every element $x$ of $G$ not lying in $N$ , the elements in the coset $x N$ all have the same…

math.GR2025

$M$ -groups and Codegrees; $M_{p}$ -groups and Brauer Character Degrees

Xiaoyou Chen, Mark L. Lewis

Let $G$ be a finite group and $p$ be a prime. We prove that if $G$ has three codegrees, then $G$ is an $M$ -group. We prove for some prime $p$ that if every irreducible Brauer chara…

math.GR2025

Semi-extraspecial $p$ -groups with automorphisms of large order

Sofia Brenner, Rachel D. Camina, Mark L. Lewis

In this paper, we consider semi-extraspecial $p$ -groups $G$ that have an automorphism of order $∣ G : G^{'} ∣ - 1$ . We prove that these groups are isomorphic to Sylow $p$ -subgroups of ${\…

math.GR2024

On non self-normalizing subgroups

Mariagrazia Bianchi, Rachel D. Camina, Mark L. Lewis +2

Let $n$ be a non negative integer, and define $D_{n}$ to be the family of all finite groups having precisely $n$ conjugacy classes of nontrivial subgroups that are not self-normalizi…

math.GR2024

Groups with a Fixed Character Degree

Mark L. Lewis, Brandon Martin

This note is concerned with the question: for which positive integers $d, e$ , with $d$ square-free and $gcd (d, d + e) = 1$ , does there exist a solvable (we will see, in our case,…

math.GR2024

On common zeros of characters of finite groups

Mark L. Lewis, Lucia Morotti, Emanuele Pacifici +2

Let $G$ be a finite group, and let $Irr (G)$ denote the set of the irreducible complex characters of $G$ . An element $g \in G$ is called a vanishing element of $G$ if there ex…

math.GR2024

Some results on the norm of finite groups

Mark L. Lewis, Zhencai Shen, Quanfu Yan

Let $G$ be a finite group and $N_{Ω} (G)$ be the intersection of the normalizers of all subgroups belonging to the set $Ω (G),$ where $Ω (G)$ is a set of all subgroups of $G$ which have…

math.GR2024

On the group pseudo-algebra of finite groups

Mark L. Lewis, Quanfu Yan

Let $G$ be a finite group. The group pseudo-algebra of $G$ is defined as the multi-set $C (G) = {(d, m_{G} (d)) ∣ d \in Cod (G)},$ where $m_{G} (d)$ is the number of irreducible chara…

math.GR2024

A note on the codegree of finite groups

Mark L. Lewis, Quanfu Yan

Let $χ$ be an irreducible character of a group $G,$ and $S_{c} (G) = \sum_{χ \in Irr (G)} cod (χ)$ be the sum of the codegrees of the irreducible characters of $G .$ Write ${\rm…

math.GR2024

On the sum of character codegrees of finite groups

Mark L. Lewis, Quanfu Yan

Let $χ$ be an irreducible character of a group $G .$ We denote the sum of the codegrees of the irreducible characters of $G$ by $S_{c} (G) = \sum_{χ \in Irr (G)} cod (χ) .$ We con…

math.GR2024

A lower bound on the size of maximal abelian subgroups

Mark L. Lewis

Let $G$ be a $p$ -group for some prime $p$ . Let $n$ be the positive integer so that $∣ G : Z (G) ∣ = p^{n}$ . Suppose $A$ is a maximal abelian subgroup of $G$ . Let $$p^l = {\rm max} \{|Z(C_…

math.GR2024

Characterizing finite groups whose enhanced power graphs have universal vertices

David G. Costanzo, Mark L. Lewis, Stefano Schmidt +2

Let $G$ be a finite group and construct a graph $Δ (G)$ by taking $G ∖ {1}$ as the vertex set of $Δ (G)$ and by drawing an edge between two vertices $x$ and $y$ if $\langle x…

Groups with a Fixed Character Degree: The General Case

The category of centralizer lattices of groups

Groups with a conjugacy class that is the difference of two normal subgroups

Sylow subgroups and the number of irreducible characters of degrees divisible by a prime p

Groups Having a Character of Maximal Degree

Group cosets with all elements of equal order

M-groups and Codegrees; Mp​-groups and Brauer Character Degrees

Semi-extraspecial p-groups with automorphisms of large order

On non self-normalizing subgroups

Groups with a Fixed Character Degree

On common zeros of characters of finite groups

Some results on the norm of finite groups

On the group pseudo-algebra of finite groups

A note on the codegree of finite groups

On the sum of character codegrees of finite groups

A lower bound on the size of maximal abelian subgroups

Characterizing finite groups whose enhanced power graphs have universal vertices

Sylow subgroups and the number of irreducible characters of degrees divisible by a prime $p$

$M$ -groups and Codegrees; $M_{p}$ -groups and Brauer Character Degrees

Semi-extraspecial $p$ -groups with automorphisms of large order