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Construction of nonisomorphic reverse steiner quasigroups

โœ Scribed by Charles C. Lindner

Publisher
Elsevier Science
Year
1974
Tongue
English
Weight
502 KB
Volume
7
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

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 contains an involution fixing exactly one element. The spectrum for reverse Steiner quasigroups has recently been shown to be the set of all positive integers such that n = 1, 3,9 cr 19 (mod 24). This paper gives a new construction for reverse Steiner quasigroups and is used to construct large numbers of nonisomorphic reverse Steiner quasigroups. (For example, lOso nonisomorphic reverse Steiner quasigroups >f ardor 171.

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