Quasigroup Identities and Mendelsohn Designs
- 1 April 1989
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 41 (2) , 341-368
- https://doi.org/10.4153/cjm-1989-017-0
Abstract
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.Keywords
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