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arXiv · 2301.02365

On the Characterization of Sporadic Simple Groups by Codegrees

Mallory Dolorfino·Luke Martin·Zachary Slonim·Yuxuan Sun·Yong Yang
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Abstract

Let $G$ be a finite group and $\mathrm{Irr}(G)$ the set of all irreducible complex characters of $G$. Define the codegree of $\chi \in \mathrm{Irr}(G)$ as $\mathrm{cod}(\chi):=\frac{|G:\mathrm{ker}(\chi) |}{\chi(1)}$ and denote by $\mathrm{cod}(G):=\{\mathrm{cod}(\chi)|\chi\in \mathrm{Irr}(G)\}$ the codegree set of $G$. Let $H$ be one of the $26$ sporadic simple groups. In this paper, we show that $H$ is determined up to isomorphism by cod$(H)$.

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Mallory Dolorfino, Luke Martin, Zachary Slonim, Yuxuan Sun, Yong Yang. 2023-01-06. On the Characterization of Sporadic Simple Groups by Codegrees. https://arxiv.org/abs/2301.02365

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