On free products of right ordered groups with amalgamated subgroups

Abstract

Abstract We prove a theorem that implies: Let G 1 =〈 G 1 , ⋅, ≤〉 and G 2 =〈 G 2 , ⋅, ≤〉 be ordered groups with subgroups H 1 and H 2 , respectively . If ϕ : H 1 ≅ H 2 is an order-preserving isomorphism, then the free product of G 1 and G 2 with H 1 and H 2 amalgamated 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.