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arXiv · 2501.02294

How Associative Can a Non-Associative Moufang Loop Be?

Ilan Levin
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Abstract

We prove a non-associative analog to the well-known $\frac{5}{8}$ 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 $\frac{43}{64}$, then the loop must be a group. The bound is tight as demonstrated by the 16-element Octonion loop.

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Ilan Levin. 2025-01-04. How Associative Can a Non-Associative Moufang Loop Be?. https://arxiv.org/abs/2501.02294

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