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Distributive and trimedial quasigroups of order 243
- Publication Year :
- 2016
-
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}.
- Subjects :
- Mathematics - Group Theory
20N05 (Primary), 05B15, 05B07 (Secondary)
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1603.00608
- Document Type :
- Working Paper