Article contents
On free products of right ordered groups with amalgamated subgroups
Published online by Cambridge University Press: 01 May 2009
Abstract
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.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 146 , Issue 3 , May 2009 , pp. 591 - 601
- Copyright
- Copyright © Cambridge Philosophical Society 2008
References
REFERENCES
- 6
- Cited by