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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 agroupoid and a commutative semigroup. In this note, we show thatif G is a finite AG-groupoid with a left zero then, undercertain conditions, G without the left zero element is a commutative group

Finite AG-groupoid with left identity and left zero