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Proceedings of the London Mathematical Society Advance Access originally published online on April 24, 2009
Proceedings of the London Mathematical Society 2009 99(3):585-608; doi:10.1112/plms/pdp008
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© 2009 London Mathematical Society

Word problems, embeddings, and free products of right-ordered groups with amalgamated subgroup

V. V. Bludov

Department of Mathematics, Physics, and Informatics
Irkutsk Teachers Training University
Irkutsk 664011
Russia
vasily-bludov@yandex.ru

A. M. W. Glass

Queens’ College,
Cambridge
CB3 9ET
United Kingdom
and
Department of Pure Mathematics and Mathematical Statistics
Centre for Mathematical Sciences
Wilberforce Road
Cambridge
CB3 0WB
United Kingdom

Received 30 September 2008. Revision received 29 January 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.

2000 Mathematics Subject Classification 06F15, 20F60, 20E06, 20B27, 20F10.

Dedicated to Graham Higman FRS, in memoriam, with gratitude for his research

This research was supported by grants from the Royal Society, the London Mathematical Society (Scheme IV, Travel) and Queens’ College, Cambridge.


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