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arXiv · 2407.16926

Commuting Involutions in Finite Simple Groups

Robert M. Guralnick·Geoffrey R. Robinson
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Abstract

We prove that if $G$ is a finite simple group and $x, y \in G$ are involutions, then $|x^G \cap C_G(y)| \rightarrow \infty$ as $|G| \rightarrow \infty$. This extends results of Guralnick-Robinson and Skresanov. We also prove a related result about $C_{G}(t)/O(C_G(t))$ that does not require the classification of finite simple groups.

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Robert M. Guralnick, Geoffrey R. Robinson. 2024-07-24. Commuting Involutions in Finite Simple Groups. https://arxiv.org/abs/2407.16926

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