M. L. Lewis

activity

20242026

collaborators

8 papers

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…

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

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