M. Lewis

activity

20242026

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9 papers · 1 filter

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…