T. Keller

activity

20232026

most citedPrime divisors and the number of conjugacy classes of finite groups

5 citations · 5 across the 8 of their papers we have counts for

collaborators

10 papers

math.GR2026

The prime graph complements of $A_{11}$ - and $A_{13}$ -solvable groups

Logan Abounader, Austin Bell, April Beun +3

We study prime graph complements of $A_{n}$ -solvable groups, focusing on the cases $A_{11}$ and $A_{13}$ . These provide the first classifications of $T$ …

math.GR2026

On the number of conjugacy classes of finite solvable groups of order divisible by $p^{2}$

Thomas Michael Keller

In 2003, Héthelyi and Külshammer proved that if $G$ is a finite solvable group and $p$ is a prime such that $p^{2}$ divides $∣ G ∣$ , then $k (G) \geq (49 p + 1) /60$ , and they constructed an…

math.GR2025

Realizing Gruenberg-Kegel graphs of $T$ -solvable groups with structurally simplified extensions of $T$

Lucas Alland, Andrei Fridman, Thomas Michael Keller

Given a finite group $G$ , its prime graph $Γ (G)$ (also known as its Gruenberg-Kegel graph) is the graph whose vertices are the prime divisors of $∣ G ∣$ and where edges ${p, q}$ ex…

math.GR2025

Criteria for Classifying Prime Graphs of PSL(2, q)-Solvable Groups

Thomas Michael Keller, Zachary Martin, Alexa Renner +2

For a finite group $G$ , the prime graph $Γ (G)$ (also known as Gruenberg-Kegel graph) is defined to be the graph where the vertices are the primes that divide $∣ G ∣$ such that two ve…

math.GR2024

Classification of the Prime Graphs of $Sz (8)$ -, $Sz (32)$ -, and $PSL (2, 2^{5})$ -Solvable Groups

Thomas Michael Keller, Zachary Martin, Alexa Renner +2

For a finite group $G$ , the vertices of the prime graph $Γ (G)$ are the primes that divide $∣ G ∣$ , and two vertices $p$ and $q$ are connected by an edge if there is an element of ord…

math.GR2024

Classifying prime graphs of finite groups -- a methodical approach

Thomas Michael Keller, Gavin Pettigrew, Saskia Solotko +1

For a finite group $G$ , the vertices of the prime graph $Γ (G)$ are the primes that divide $∣ G ∣$ , and two vertices $p$ and $q$ are connected by an edge if and only if there is an el…

math.GR2024

More on Landau's theorem and Conjugacy Classes

Burcu Çınarcı, Thomas Michael Keller, Attila Maróti +1

In this paper we present two new results on the number of certain conjugacy classes of a finite group. For a finite group $G$ , let $n (G)$ be the maximum of $k_{p} (G)$ taken over al…

math.GR2023

Bounding the number of p'-degrees from below

Thomas Keller, Yong Yang

Let $G$ be a finite group of order divisible by a prime $p$ and let $P\in\Syl_p(G)$. We prove a recent conjecture by Hung stating that $|\Irr_{p'}(G)|\geq \frac{\exp(P/P')-1}{p-1}+…

math.GR2023

A new lower bound for the number of conjugacy classes

Burcu Çınarcı, Thomas Michael Keller

In 2003, Héthelyi and Külshammer proposed that if $G$ is a finite group and $p$ is a prime dividing the group order, then $k (G) \geq 2 p - 1$ , and they proved this conjecture fo…

math.GR2023★ 5 cited

Prime divisors and the number of conjugacy classes of finite groups

Thomas Michael Keller, Alexander Moretó

We prove that there exists a universal constant $D$ such that if $p$ is a prime divisor of the index of the Fitting subgroup of a finite group $G$ , then the number of conjugacy cla…

The prime graph complements of A11​- and A13​-solvable groups

On the number of conjugacy classes of finite solvable groups of order divisible by p2

Realizing Gruenberg-Kegel graphs of T-solvable groups with structurally simplified extensions of T

Criteria for Classifying Prime Graphs of PSL(2, q)-Solvable Groups

Classification of the Prime Graphs of Sz(8)-, Sz(32)-, and PSL(2,25)-Solvable Groups

Classifying prime graphs of finite groups -- a methodical approach

More on Landau's theorem and Conjugacy Classes

Bounding the number of p'-degrees from below

A new lower bound for the number of conjugacy classes

Prime divisors and the number of conjugacy classes of finite groups

The prime graph complements of $A_{11}$ - and $A_{13}$ -solvable groups

On the number of conjugacy classes of finite solvable groups of order divisible by $p^{2}$

Realizing Gruenberg-Kegel graphs of $T$ -solvable groups with structurally simplified extensions of $T$

Classification of the Prime Graphs of $Sz (8)$ -, $Sz (32)$ -, and $PSL (2, 2^{5})$ -Solvable Groups