A groupoidGwhose elements satisfy the left invertive law:(ab)c=(cb)ais 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 ifGis a finite AG-groupoid with a left zero then, under certain conditions,Gwithout the left zero element is a commutative group.
Finite AG-groupoid with left identity and left zero
