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arXiv · 2201.09402

Limit Points of Commuting Probabilities of Finite Groups

Thomas Browning
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Abstract

The commuting probability of a finite group $G$ is the probability that two randomly chosen elements commute. Let $S\subseteq(0,1]$ denote the set of all possible commuting probabilities of finite groups. We prove that $S\cup\{0\}$ is closed, which was conjectured by Keith Joseph in 1977.

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Thomas Browning. 2022-01-24. Limit Points of Commuting Probabilities of Finite Groups. https://arxiv.org/abs/2201.09402

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