A classification of abelian quasigroups

Abstract

We extend the classification of abelian quasigroups from isotopy classes, which was done in [2] and [9], to isomorphy classes. For this purpose we use the concept of an extended triple system in order to state our results.

Keywords

• abelian quasigroups
• totally symmetric quasigroups
• entropic law
• extended triple systems
• elliptic curves