We prove a theorem that implies:
Let G1=〈G1, ⋅, ≤〉 andG2=〈G2, ⋅, ≤〉 be ordered groups with subgroupsH1andH2, respectively. If ϕ : H1 ≅ H2is an order-preserving isomorphism, then the free product ofG1andG2withH1andH2amalgamated via ϕ is right orderable.
This solves Problem 15⋅34 from the Kourovka Notebook.
We extend this result to an arbitrary family of ordered groups with order-preserving-isomorphic subgroups amalgamated.