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On free products of right ordered groups with amalgamated subgroups

Published online by Cambridge University Press:  01 May 2009

V. V. BLUDOV  and
A. M. W. GLASS
V. V. BLUDOV
Affiliation:
Department of Mathematics, Physics, and Informatics, Irkutsk Teachers Training University, Irkutsk 664011, Russia. e-mail: vasily-bludov@yandex.ru
A. M. W. GLASS
Affiliation:
Queens' College, Cambridge CB3 9ET. and Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB. e-mail: amwg@dpmms.cam.ac.uk
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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

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References

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