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Note on Quasigroups and Trees

Published online by Cambridge University Press:  20 January 2009

I. M. H. Etherington
I. M. H. Etherington
Affiliation:
Mathematical InstituteThe University, Edinburgh
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If letters a, b, c, … are used to denote points of a nondegenerate plane cubic curve, other than the singular point if any, and if the product ab is defined as the third point of the curve collinear with a and b, we obtain an algebraic system having nonassociative multiplication (ab . c ≠ a . bc in general). It is in fact a totally symmetric entropic quasigroup (these terms are defined below). This idea, which was put forward at a meeting of the Edinburgh Mathematical Society a few years ago, will be exploited in a forthcoming paper. Such quasigroups have many properties which can be interpreted geometrically. Or, conversely, known properties of cubic curves suggest theorems about totally symmetric entropic quasigroups, which if established will involve a gain in generality, since not every such quasigroup can be “placed” on a cubic.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 13 , Issue 3 , June 1963 , pp. 219 - 222
Copyright
Copyright © Edinburgh Mathematical Society 1963

References

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