Enumerating AG-Groups with a Study of Smaradache AG-Groups

Abstract

AG-groups are a generalisation of Abelian groups. They correspond to groupoids with a left identity, unique inverses, and satisfy the identity (xy)z = (zy)x. We present the first enumeration result for AG-groups up to order 11 and give a lower bound for order 12. The counting is performed with the finite domain enumerator FINDER using bespoke symmetry breaking techniques. We have also developed a function in the GAP computer algebra system to check the generated Cayley tables. This note discusses a few observations obtained from our results, some of which inspired us to examine and discuss Smaradache AG-group structures.