Abstract

A groupoid G whose elements satisfy the left invertive law: (ab)c=(cb)a is known as Abel-Grassman's groupoid (AG-groupoid). It is a nonassociative algebraic structure midway between a groupoid and a commutative semigroup. In this note, we show that if G is a finite AG-groupoid with a left zero then, under certain conditions, G without the left zero element is a commutative group.