How Associative Can a Non-Associative Moufang Loop Be?

2025/01/04 by Levin, Ilan
Psychology · #05E16 #60B99 #Categorization, perception, and language #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Primary: 20N05 #Probability (math.PR) #Secondary: 05B07

paper · pdf · doi:10.48550/arxiv.2501.02294

openalex publication_date 2025/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a non-associative analog to the well-known (5)/(8) Theorem. Namely, for a finite Moufang loop with nuclear commutators, we show that if the probability that three randomly chosen elements associate is greater than (43)/(64), then the loop must be a group. The bound is tight as demonstrated by the 16-element Octonion loop.

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