Distributive and trimedial quasigroups of order 243

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• 作者：Přemysl Jedlička^a ; ^{jedlickap@tf.czu.cz} ; David Stanovský ; ^b ; ^c ; ^{stanovsk@karlin.mff.cuni.cz} ; Petr Vojtěchovský ; ^d ; ^{petr@math.du.edu}
• 关键词：Distributive quasigroup ; Trimedial quasigroup ; Medial quasigroup ; Entropic quasigroup ; Commutative Moufang loop ; Latin square ; Mendelsohn triple system ; Classification ; Enumeration
• 刊名：Discrete Mathematics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：340
• 期：3
• 页码：404-415
• 全文大小：474 K
• 卷排序：340

文摘

We enumerate three classes of non-medial quasigroups of order 243=35243=35 up to isomorphism. There are 17004 non-medial trimedial quasigroups of order 243243 (extending the work of Kepka, Bénéteau and Lacaze), 9292 non-medial distributive quasigroups of order 243243 (extending the work of Kepka and Němec), and 66 non-medial distributive Mendelsohn quasigroups of order 243243 (extending the work of Donovan, Griggs, McCourt, Opršal and Stanovský).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 LOOPS package in GAP.