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Comptes Rendus Mathématique
Volume 346, n° 3-4
pages 173-176 (février 2008)
Doi : 10.1016/j.crma.2007.11.027
Received : 12 November 2007 ;  accepted : 22 November 2007
Proper actions of lamplighter groups associated with free groups
Actions propres du groupe de l’allumeur de réverbères associé au groupe libre

Yves de Cornulier a , Yves Stalder b , Alain Valette c
a Institut de recherche mathématique de Rennes, Université de Rennes 1, campus de Beaulieu, 35042 Rennes cedex, France 
b Laboratoire de mathématiques, Université Blaise-Pascal, campus universitaire des Cézeaux, 63177 Aubière cedex, France 
c Institut de mathématiques, Université de Neuchâtel, rue Émile-Argand 11, CP 158, CH-2009 Neuchâtel, Switzerland 


Given a finite group H and a free group  , we prove that the wreath product   admits a metrically proper, isometric action on a Hilbert space. To cite this article: Y. de Cornulier et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).

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Soit H un groupe fini et F un groupe libre, ou plus généralement un groupe admettant une structure d’espace à murs invariante à gauche et propre. Nous montrons que le produit en couronne   admet également une telle structure d’espace à murs. En conséquence, il a la propriété de Haagerup, c’est-à-dire qu’il possède une action isométrique métriquement propre sur un espace de Hilbert. Pour citer cet article : Y. de Cornulier et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).

The full text of this article is available in PDF format.

 This research was performed at Centre Bernoulli (EPF Lausanne), in the framework of the semester “Limits of graphs in group theory and computer science”.

© 2007  Académie des sciences@@#104156@@
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