Let Fix, y) be the free groupoid on two generators x and y. Define an infinite class of words in F(x, y) by WO(X, y) = X, WI (x, y) = y and ~f+2t~, y) -Wi(X, y) wi+ 1(x, y). An identity of the form \v~~(x, y) = x is called a cyclic identity and ;f quasigroup satisfying a cyclic identity is called a
On the construction of Schroeder quasigroups
β Scribed by C.C. Lindner; N.S. Mendelsohn; S.R. Sun
- Publisher
- Elsevier Science
- Year
- 1980
- Tongue
- English
- Weight
- 377 KB
- Volume
- 32
- Category
- Article
- ISSN
- 0012-365X
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π SIMILAR VOLUMES
4 Steiner quasigroup is a quasigroup satisfying the identities x (xy) = y, (JX)X = y and x2 = X. It is well known that the spectrum for Steiner quasi:j:roups is the set of all positive integers such that n = 1 or 3 (mod 6). A Steiner quasigroup is reverse provided that its automorphism group contain
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 integer