Elements of finite order in automorphism groups of homogeneous structures
DOI:
https://doi.org/10.11575/cdm.v8i2.62171Keywords:
Homogeneous structures, Fraïssé classes, Baire categoryAbstract
We study properties of the automorphism groups of Fraïssé limits of classes with certain strong amalgamation properties, including classes with the free amalgamation property and classes of metric spaces. We discuss conditions on aFraïssé class $ that imply that the automorphism group of its limit admits generic elements of order n for all n, and show that, for many such classes, any element of the automorphism group is a product of 4 conjugates of the generic element of order n for alln greater than 2. Our constructions enable us to compute the Borel complexity of the relation of conjugacy between automorphisms of the Henson graphs, and to obtain some new results about the structure of the isometry group of the Urysohn space and the Urysohn sphere.Downloads
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