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Automorphism groups of trivial strongly minimal structures

Published online by Cambridge University Press:  12 March 2014

Thomas Blossier
Thomas Blossier*
Affiliation:
Ufr de Mathématiques, Université Lyon I, Bâtiment Doyen Jean Braconnier, 21 Avenue Claude Bernard, 69622 Villeurbanne Cedex, France, E-mail: blossier@igd.univ-lyonl.fr
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Abstract

We study automorphism groups of trivial strongly minimal structures. First we give a characterization of structures of bounded valency through their groups of automorphisms. Then we characterize the triplets of groups which can be realized as the automorphism group of a non algebraic component, the subgroup stabilizer of a point and the subgroup of strong automorphisms in a trivial strongly minimal structure, and also we give a reconstruction result. Finally, using HNN extensions we show that any profinite group can be realized as the stabilizer of a point in a strongly minimal structure of bounded valency.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 68 , Issue 2 , June 2003 , pp. 644 - 668
Copyright
Copyright © Association for Symbolic Logic 2003

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References

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