Zachary Slonim

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20222026

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4 papers · 1 filter

math.GR2023

Characterization of Solubilizers of Elements in Minimal Simple Groups

Banafsheh Akbari, Jake Chuharski, Vismay Sharan +1

Given a finite group $G$ , the solubilizer of an element $x$ , denoted by $\Sol_G(x)$, is the set of all elements $y$ such that $⟨ x, y ⟩$ is a soluble subgroup of $G$ . In…

math.GR2023

On the Characterization of Sporadic Simple Groups by Codegrees

Mallory Dolorfino, Luke Martin, Zachary Slonim +2

Let $G$ be a finite group and $Irr (G)$ the set of all irreducible complex characters of $G$ . Define the codegree of $χ \in Irr (G)$ as $\mathrm{cod}(χ):=\frac{|G:\m…

math.GR2023

On the Characterization of Alternating Groups by Codegrees

Mallory Dolorfino, Luke Martin, Zachary Slonim +2

Let $G$ be a finite group and $Irr (G)$ the set of all irreducible complex characters of $G$ . Define the codegree of $χ \in Irr (G)$ as $\mathrm{cod}(χ):=\frac{|G:\m…

math.GR2022

Classifying Solvable Primitive Permutation Groups of Low Rank

Mallory Dolorfino, Luke Martin, Zachary Slonim +2

Suppose that $G$ is a finite, transitive, solvable permutation group acting on a set $S$ with $n$ elements. Let $G_{0}$ be the stabilizer of a point $α \in Ω$ . Define the rank of a pe…