Special-valued subgroups of lattice-ordered groups

We prove that the intersection of all maximal special-valued subgroups of a lattice-ordered group $G$ is the special-valued quasi-torsion radical of a lattice-ordered group $G$, which extends our earlier result that the intersection of all maximal finite-valued subgroups of a lattice-ordered group $G$ is the finite-valued torsion radical of $G$. We also show that the class $A_f$ of almost finite-valued lattice-ordered groups is a quasi-torsion class, and the $A_f$ quasi-torsion radical of a group is equal to the intersection of the group with the lateral completion of the finite-valued torsion radical of the group.