Journal of Symbolic Logic

Recovering ordered structures from quotients of their automorphism groups

M. Giraudet and J. K. Truss

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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

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

First available in Project Euclid: 31 October 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

chain doubly homogeneous chain countable cofinality quotient recovery


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.

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