Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.02294 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917883575009280 |
|---|---|
| author | Levin, Ilan |
| author_facet | Levin, Ilan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02294 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | How Associative Can a Non-Associative Moufang Loop Be? Levin, Ilan Group Theory Combinatorics Probability Primary: 20N05, Secondary: 05B07, 05E16, 60B99 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. |
| title | How Associative Can a Non-Associative Moufang Loop Be? |
| topic | Group Theory Combinatorics Probability Primary: 20N05, Secondary: 05B07, 05E16, 60B99 |
| url | https://arxiv.org/abs/2501.02294 |