A commutative BCK-algebra has the relative cancellation property if for \(x,y\geq a\), \(x*a= y*a\) implies that \(x=y\). Any upwards directed commutative BCK-algebra has this property. The authors consider imbeddings of such algebras into Abelian lattice-ordered groups, and universal groups for the BCK-clans derived from the BCK-algebras.