A Moufang loop with exceptional properties of associators

2015/09/02 by Ilya Gorshkov, Ilya B. Gorshkov, Gorshkov, Ilya B. +4
Engineering · Mathematics · #20N05 #FOS: Mathematics #Group Theory (math.GR) #Mathematics and Applications #graph theory and CDMA systems #math.GR #msc:20N05

paper · pdf · doi:10.48550/arxiv.1509.00559

arxiv created 2015/09/02 · openalex publication_date 2015/09/02 · arxiv updated 2015/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a Moufang loop M of order 3¹⁹ and a pair a,b of its elements such that the set of all elements of M that associate with a and b does not form a subloop. This is also an example of a nonassociative Moufang loop with a generating set whose every three elements associate.

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