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

Fundamenta Mathematicae (2016)

- Volume: 232, Issue: 1, page 49-63
- ISSN: 0016-2736

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topDavid M. Evans, and Todor Tsankov. "Free actions of free groups on countable structures and property (T)." Fundamenta Mathematicae 232.1 (2016): 49-63. <http://eudml.org/doc/282791>.

@article{DavidM2016,

abstract = {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.},

author = {David M. Evans, Todor Tsankov},

journal = {Fundamenta Mathematicae},

keywords = {oligomorphic groups; property (T); omega-categoricity; unitary representations; Roelcke precompact},

language = {eng},

number = {1},

pages = {49-63},

title = {Free actions of free groups on countable structures and property (T)},

url = {http://eudml.org/doc/282791},

volume = {232},

year = {2016},

}

TY - JOUR

AU - David M. Evans

AU - Todor Tsankov

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

JO - Fundamenta Mathematicae

PY - 2016

VL - 232

IS - 1

SP - 49

EP - 63

AB - 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.

LA - eng

KW - oligomorphic groups; property (T); omega-categoricity; unitary representations; Roelcke precompact

UR - http://eudml.org/doc/282791

ER -

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