Journal of Symbolic Logic

Recovering ordered structures from quotients of their automorphism groups

M. Giraudet and J. K. Truss

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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.

Article information

Source
J. Symbolic Logic, Volume 68, Issue 4 (2003), 1189-1198.

Dates
First available in Project Euclid: 31 October 2003

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1067620181

Digital Object Identifier
doi:10.2178/jsl/1067620181

Mathematical Reviews number (MathSciNet)
MR2017349

Zentralblatt MATH identifier
1076.06010

Subjects
Primary: 06F15: Ordered groups [See also 20F60] 20F60: Ordered groups [See mainly 06F15]

Keywords
chain doubly homogeneous chain countable cofinality quotient recovery

Citation

Giraudet, M.; Truss, J. K. Recovering ordered structures from quotients of their automorphism groups. J. Symbolic Logic 68 (2003), no. 4, 1189--1198. doi:10.2178/jsl/1067620181. https://projecteuclid.org/euclid.jsl/1067620181


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References

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