Commuting Involutions in Finite Simple Groups
Year: 2024
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Guralnick, Robert M., Robinson, Geoffrey R.
Institutions: University of Southern California, University of Aberdeen
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6947893076
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