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arXiv · 1603.00608

Distributive and trimedial quasigroups of order 243

Přemysl Jedlička·David Stanovský·Petr Vojtěchovský
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Abstract

We enumerate three classes of non-medial quasigroups of order $243=3^5$ up to isomorphism. There are $17004$ non-medial trimedial quasigroups of order $243$ (extending the work of Kepka, B\'en\'eteau and Lacaze), $92$ non-medial distributive quasigroups of order $243$ (extending the work of Kepka and N\v{e}mec), and $6$ non-medial distributive Mendelsohn quasigroups of order $243$ (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}.

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Přemysl Jedlička, David Stanovský, Petr Vojtěchovský. 2016-03-02. Distributive and trimedial quasigroups of order 243. https://arxiv.org/abs/1603.00608

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