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On the spectrum of Stein quasigroups

Published online by Cambridge University Press:  17 April 2009

F.E. Bennett  and
N.S. Mendelsohn
F.E. Bennett
Affiliation:
Department of Mathematics and Astronomy, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2.
N.S. Mendelsohn
Affiliation:
Department of Mathematics and Astronomy, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2.
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Abstract

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In this paper we investigate the spectrum of a variety of quasigroups satisfying the 2-variable identity x(xy) = yx, called Stein quasigroups. Stein quasigroups are known to be self-orthogonal and have been given a considerable amount of attention because of this property. It is known that there are no Stein quasigroups of order 2, 3, 6, 7, 8, 10, 12, 14. The object of this paper is to show that for all but 36 values of n ≥ 15 there exists a Stein quasigroup of order n. In particular, the spectrum of Stein quasigroups contains all n ≥ 191.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 21 , Issue 1 , February 1980 , pp. 47 - 63
Copyright
Copyright © Australian Mathematical Society 1980

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