## Abstract We present the numbers of isotopy classes and main classes of Latin squares, and the numbers of isomorphism classes of quasigroups and loops, up to order 10. The best previous results were for Latin squares of order 8 (Kolesova, Lam, and Thiel, 1990), quasigroups of order 6 (Bower, 2000
β¦ LIBER β¦
Quasigroups, Loops, and Associative Laws
β Scribed by Kenneth Kunen
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 140 KB
- Volume
- 185
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
β¦ Synopsis
We investigate the question of which weakenings of the associative law imply that a quasigroup is a loop. In particular, we completely settle the question for all Ε½ laws of ''BolαMoufang type'' those written with four variables, three of which are . distinct .
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