The product of divisibility groups with G1 finitely generated

We show that: (1) If is a finitely generated divisibility group that is not lattice ordered and if is a divisibility group such that , then the product is not a divisibility group. (2) If is a torsion free finitely generated divisibility group and if is a lattice ordered group with only finitely many ultra filters, then the product is a divisibility group if and only if . (3) If and are both torsion free finitely generated divisibility groups, then the product is a divisibility group.