Limit Points of Commuting Probabilities of Finite Groups

2022/01/24 by Thomas Browning, Browning, Thomas
Computer Science · Mathematics · #Advanced Graph Theory Research #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2201.09402

openalex publication_date 2022/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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