T. Keller

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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 $I^ (G)$ (also known as its Gruenberg-Kegel graph) is the graph whose vertices are the prime divisors of $∣ G ∣$ and where edges ${p, q}$ e…

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 $I^ (G)$ (also known as Gruenberg-Kegel graph) is defined to be the graph where the vertices are the primes that divide $∣ G ∣$ such that two v…

math.GR2025

More on Landau's theorem and Conjugacy Classes

Burcu ÃÄ±narcÄ±, Thomas Michael Keller, Attila MarÃ³ti +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.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 $I^ (G)$ are the primes that divide $∣ G ∣$ , and two vertices $p$ and $q$ are connected by an edge if there is an element of or…

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 $I^ (G)$ are the primes that divide $∣ G ∣$ , and two vertices $p$ and $q$ are connected by an edge if and only if there is an e…

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

More on Landau's theorem and Conjugacy Classes

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

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