Author

Alexa Renner

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Preprint Oct 2026

Prime Graphs of Infinite Groups

The prime graph of a finite group $G$ is the graph $\Gamma(G)$ with vertex set the set of prime divisors $\pi(G)$ of $|G|$ and an edge between vertices $p, q\in\pi(G)$ if and only if there exists an element $g\in G$ with order $o(g) = pq$. Given a finite nonabelian simple group $T$, a group $G$ is $T$-solvable if there...

Alexa Renner · 0 citations

Preprint Aug 2026

Decidability of the Orbit Problem Over $\mathbb{Q}(X)$

The orbit problem is the problem of whether, given $x, y\in \mathbb{Q}^n$ and an $n\times n$ matrix $A$, there exists an $i\in\mathbb{N}$ such that $A^ix = y$. In 1980, Kannan and Lipton proved that the orbit problem is decidable. We show that a generalization of the orbit problem, where the field is $\mathbb{Q}(X)$ fo...

Joshua Holden, Alexa Renner · 0 citations