Distributive and trimedial quasigroups of order 243
Group Theory
2016-07-18 v2
Abstract
We enumerate three classes of non-medial quasigroups of order up to isomorphism. There are non-medial trimedial quasigroups of order (extending the work of Kepka, B\'en\'eteau and Lacaze), non-medial distributive quasigroups of order (extending the work of Kepka and N\v{e}mec), and non-medial distributive Mendelsohn quasigroups of order (extending the work of Donovan, Griggs, McCourt, Opr\v{s}al and Stanovsk\'y). The enumeration technique is based on affine representations over commutative Moufang loops, on properties of automorphism groups of commutative Moufang loops, and on computer calculations with the \texttt{LOOPS} package in \texttt{GAP}.
Keywords
Cite
@article{arxiv.1603.00608,
title = {Distributive and trimedial quasigroups of order 243},
author = {Přemysl Jedlička and David Stanovský and Petr Vojtěchovský},
journal= {arXiv preprint arXiv:1603.00608},
year = {2016}
}