## Abstract A ternary quasigroup (or 3βquasigroup) is a pair (__N, q__) where __N__ is an __n__βset and __q__(__x, y, z__) is a ternary operation on __N__ with unique solvability. A 3βquasigroup is called 2βidempotent if it satisfies the generalized idempotent law: __q__(__x, x, y__) = __q__(__x, y
The spectrum for large sets of idempotent quasigroups
β Scribed by Yanxun Chang
- Publisher
- John Wiley and Sons
- Year
- 2000
- Tongue
- English
- Weight
- 73 KB
- Volume
- 8
- Category
- Article
- ISSN
- 1063-8539
No coin nor oath required. For personal study only.
β¦ Synopsis
In this article we construct a large set of idempotent quasigroups of order 14. Combined with the results in Chang, JCMCC; and Teirlinck and Lindner, Eur J Combin 9 (1988), 83Β±89, this shows that the spectrum for large sets of idempotent quasigroups of order n [brieΒ―y, LIQ(n)] is the set all integers n ! 3 with the exception of n 6.
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