How Associative Can a Non-Associative Moufang Loop Be?
Group Theory
2025-01-07 v1 Combinatorics
Probability
Abstract
We prove a non-associative analog to the well-known 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 , then the loop must be a group. The bound is tight as demonstrated by the 16-element Octonion loop.
Cite
@article{arxiv.2501.02294,
title = {How Associative Can a Non-Associative Moufang Loop Be?},
author = {Ilan Levin},
journal= {arXiv preprint arXiv:2501.02294},
year = {2025}
}