M. Lewis

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20242026

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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 ${\…

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

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