Abelian and symmetric generalized digroups

In this paper we extend some group-like concepts to generalized digroups. We exhibit examples of non-abelian cyclic generalized digroups. We show that abelian generalized digroups are tightly related to left commutative semigroups with left identities and right inverses, and characterize these semigroups using generalized digroups properties. We also present symmetric generalized digroups and the transformation generalized digroup.