Generalised lattice ordered groups (gl-groups)

In this paper introduced the concept of generalised lattice orderedgroup (gl-group) in such a way that every l-group is a gl-group but theconverse is not true. Proved that every gmsl-group (gjsl-group) is a glgroup.Obtained necessary and sufficient condition for the lexicographicproduct of two non-trivial directed po-groups to be a gl-group.