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Quasigroup Identities and Mendelsohn Designs

Published online by Cambridge University Press:  20 November 2018

F. E. Bennett
F. E. Bennett*
Affiliation:
Mount Saint Vincent University, Halifax, Nova Scotia
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A quasigroup is an ordered pair (Q, •), where Q is a set and (•) is a binary operation on Q such that the equations ax — b and ya — b are uniquely solvable for every pair of elements a,b in Q. It is well-known (see, for example, [11]) that the multiplication table of a quasigroup defines a Latinsquare, that is, a Latin square can be viewed as the multiplication table of a quasigroup with the headline and sideline removed. We are concerned mainly with finite quasigroups in this paper. A quasigroup (Q, •) is called idempotent if the identity x2 = x holds for all x in Q.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 41 , Issue 2 , 01 April 1989 , pp. 341 - 368
Copyright
Copyright © Canadian Mathematical Society 1989

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