Elements of finite order in automorphism groups of homogeneous structures

Dogan Bilge (1) , Julien Melleray (1)

1 ICJ - Institut Camille Jordan

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 a Fraïssé 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 corresponding automorphism group is a product of at most four conjugates of the generic element of order n for all n 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.

Domaines: Logique [math.LO]

Dogan Bilge, Julien Melleray. Elements of finite order in automorphism groups of homogeneous structures. Contributions to Discrete Mathematics, 2013, http://cdm.math.ucalgary.ca/cdm/index.php/cdm/article/view/367. ⟨hal-00713430⟩