ON SINGLE LAWS FOR VARIETIES OF QUASIGROUPS ASSOCIATED WITH EXTENDED CYCLE SYSTEMS

Abstract

It has been previously shown by Lindner and Rodger that quasigroups associated with 2-perfect extended m-cycle systems can be equationally defined if and only if m ∈ {3, 5, 7}. In this paper we present a single identity for each such m which is equivalent to the identities given for these varieties.

^*Research supported by Australian Research Council grant A69701550.

Keywords:

• 2-perfect extended m-cycle systems
• Single laws
• Varieties of groupoids

Acknowledgments

Notes

^*Research supported by Australian Research Council grant A69701550.