Exercise 23, § 1

Let G be the lattice ordered group $\mathbf{Z} \times \mathbf{Z}$ (where $\mathbf{Z}$ has the usual ordering) and H the convex subgroup of G generated by $(2, -3)$; show that the ordered group $G/H$ is not lattice orderable (cf. VI, p. 30, Ex. 4).