Completion of Linearly Ordered Metabelian Groups

We prove a theorem saying that in finitely generated linearly ordered metabelian groups there exists a finite system of normal convex subgroups satisfying orderability conditions for groups, and an embedding theorem for linearly ordered metabelian groups whose initial linear orders extend to $\Gamma$-divisible linearly ordered metabelian ones. As a consequence, it is stated that orderable metabelian groups are embedded, with extension of all their linear orders, in $\Gamma$-divisible orderable metabelian groups.