Limit points in the range of the commuting probability function on finite groups

2012/07/03 by Peter Hegarty, Hegarty, Peter
Mathematics · #20D99 #20E34 #20E45 #20P99 #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Group Theory (math.GR) #Limits and Structures in Graph Theory #math.GR #msc:20D99 #msc:20E34 #msc:20E45 #msc:20P99

paper · pdf · doi:10.48550/arxiv.1207.0760

11 pages, no figures

arxiv created 2012/07/03 · openalex publication_date 2012/07/03 · arxiv updated 2012/07/04 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

If G is a finite group, then Pr(G) denotes the fraction of ordered pairs of elements of G which commute. We show that, if l ∈ (2/9,1] is a limit point of the function Pr on finite groups, then l ∈ \Q and there exists an e = e_l > 0 such that Pr(G) \not∈ (l - e_l, l) for any finite group G. These results lend support to some old conjectures of Keith Joseph.

Citations

• What is the Probability that Two Group Elements Commute?

Related

• Limit Points of Commuting Probabilities of Finite Groups
• Commuting probability for approximate subgroups of a finite group
• On commuting probabilities in finite groups and rings
• On the commuting probability for subgroups of a finite group
• Commuting probability for conjugate subgroups of a finite group