Alexa Renner

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20242026

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math.GR2026

Prime Graphs of Locally Torsion Ultragroups, Metanilpotent Groups, and $T$ -Solvable Groups

Alexa Renner

Given a group $G$ , the prime graph of $G$ , denoted $Γ (G)$ , is the graph with vertex set the set of primes $p$ such that there exists an element of order $p$ in $G$ , and such that t…

math.GR2026

Prime Graphs of Infinite Groups

Alexa Renner

The prime graph of a finite group $G$ is the graph $Γ (G)$ with vertex set the set of prime divisors $π (G)$ of $∣ G ∣$ and an edge between vertices $p, q \in π (G)$ if and only if there…

math.GR2026

Braids on the Stranded Cellular Automata Model

Alexa Renner

The Stranded Cellular Automata (SCA) model is a grid of cells such that each cell can contain 0, 1, or 2 strands, together with two cellular automata that control when and how stra…

math.GR2026

Decidability of the Orbit Problem Over $Q (X)$

Joshua Holden, Alexa Renner

The orbit problem is the problem of whether, given $x, y \in Q^{n}$ and an $n \times n$ matrix $A$ , there exists an $i \in N$ such that $A^{i} x = y$ . In 1980, Kannan and…

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…

Prime Graphs of Locally Torsion Ultragroups, Metanilpotent Groups, and T-Solvable Groups

Prime Graphs of Infinite Groups

Braids on the Stranded Cellular Automata Model

Decidability of the Orbit Problem Over Q(X)

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

Prime Graphs of Locally Torsion Ultragroups, Metanilpotent Groups, and $T$ -Solvable Groups

Decidability of the Orbit Problem Over $Q (X)$

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