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Preprint Number 292

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292. Dugald Macpherson and Katrin Tent
Simplicity of some automorphism groups
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Submission date: 26 January 2011.

Abstract:

Let M be a countably infinite first order relational structure which is homogeneous in the sense of Fraïssé. We show, under the assumption that the class of finite substructures of M has the free amalgamation property, along with the assumption that Aut(M) is transitive on M but not equal to Sym(M), that Aut(M) is a simple group. This generalises results of Truss, Rubin and others. The proof uses the Polish group structure of the automorphism group and generalises to certain other homogeneous structures, with prospects for further application.

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