International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 6, Pages 387-389
A groupoid whose elements satisfy the left invertive law:
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 is a finite AG-groupoid with a left zero then, under
certain conditions, without the left zero element is a commutative group.