We study commutative BCK-algebras with relative cancellation
property, i.e., if $a \le x,y$, and $x \ast a = y \ast a,$
then $x = y.$ We show that any such BCK-algebra $X$ can be
embedded into the positive cone of an Abelian lattice
ordered group. Moreover, this group can be chosen to be a
universal group for $X$. Finally, we apply this result to a
special family of posets with differences and generalized
effect algebras.
