Spencer Gerhardt

activity

20162025

collaborators

5 papers

math.GR2025

Low-genus primitive monodromy groups with a nonunique minimal normal subgroup

Spencer Gerhardt, Eilidh McKemmie, Danny Neftin

Let $X$ be a Riemann surface, and let $f : X \to P_{C}^{1}$ be an indecomposable (branched) covering of genus $g$ and degree $n$ whose monodromy group has more than one m…

math.GR2021

Topological generation of simple algebraic groups

Timothy C. Burness, Spencer Gerhardt, Robert M. Guralnick

Let $G$ be a simple algebraic group over an algebraically closed field and let $X$ be an irreducible subvariety of $G^{r}$ with $r ⩾ 2$ . In this paper, we consider the genera…

math.GR2019

Topological generation of exceptional algebraic groups

Timothy C. Burness, Spencer Gerhardt, Robert M. Guralnick

Let $G$ be a simple algebraic group over an algebraically closed field $k$ and let $C_{1}, \dots, C_{t}$ be non-central conjugacy classes in $G$ . In this paper, we consider the proble…

math.GR2018

Topological generation of special linear groups

Spencer Gerhardt

Let $C_{1}, \dots, C_{e}$ be noncentral conjugacy classes of the algebraic group $G = S L_{n} (k)$ defined over a sufficiently large field $k$ , and let $Ω := C_{1} \times \dots \times C_{e}$ . This…

math.GR2016

Order three normalizers of 2-groups

Spencer Gerhardt

This paper examines order three elements of finite groups which normalize no nontrivial 2-subgroup. The motivation for finding such elements arises out of a problem in modular repr…