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Recovering ordered structures from quotients of their automorphism groups

Published online by Cambridge University Press:  12 March 2014

M. Giraudet  and
J. K. Truss
M. Giraudet
Affiliation:
Université du Maine, Faculté des Sciences, Département de Mathématiques, Avenue Olivier Messiaen, 72085 le Mans Cedex 9, France, E-mail: giraudet@logique.jussieu.fr
J. K. Truss
Affiliation:
Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, UK, E-mail: pmtjkt@leeds.ac.uk
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Abstract

We show that the ‘tail’ of a doubly homogeneous chain of countable cofinality can be recognized in the quotient of its automorphism group by the subgroup consisting of those elements whose support is bounded above. This extends the authors' earlier result establishing this for the rationals and reals. We deduce that any group is isomorphic to the outer automorphism group of some simple lattice-ordered group.

Keywords

chaindoubly homogeneous chaincountable cofinalityquotientrecovery
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 68 , Issue 4 , December 2003 , pp. 1189 - 1198
Copyright
Copyright © Association for Symbolic Logic 2003

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References

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