Word problems, embeddings, and free products of right-ordered groups with amalgamated subgroup
V. V. Bludov, A. M. W. Glass · Proceedings of the London Mathematical Society · 2009
We use permutation groups to give necessary and sufficient conditions for the free product of right-ordered groups with amalgamated subgroup to be right orderable. We obtain several consequences answering previously posed problems and also prove the right-orderable analogues of the Higman Embedding Theorem and the Boone–Higman Theorem.