Free actions of free groups on countable structures and property (T)

• Autorzy: David M. Evans , Todor Tsankov
• Języki publikacji: EN

Abstrakty

EN

We show that if G is a non-archimedean, Roelcke precompact Polish group, then G has Kazhdan's property (T). Moreover, if G has a smallest open subgroup of finite index, then G has a finite Kazhdan set. Examples of such G include automorphism groups of countable ω-categorical structures, that is, the closed, oligomorphic permutation groups on a countable set. The proof uses work of the second author on the unitary representations of such groups, together with a separation result for infinite permutation groups. The latter allows the construction of a non-abelian free subgroup of G acting freely in all infinite transitive permutation representations of G.

Kategorie tematyczne

• 22A25: Representations of general topological groups and semigroups
• 03C15: Denumerable structures
• 20B27: Infinite automorphism groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2016
• Tom: 232
• Numer: 1
• Strony: 49-63

Daty

wydano

2016

Twórcy

autor

David M. Evans

• Department of Mathematics, Imperial College London, London SW7 2AZ, UK

autor

Todor Tsankov

• Université Paris 7, UFR de Mathématiques, Case 7012, 75205 Paris Cedex 13, France

Identyfikatory

DOI

10.4064/fm232-1-4