Geometric & Functional Analysis GAFA

, Volume 13, Issue 3, pp 643–670 | Cite as

Property (T) and Kazhdan constants for discrete groups

Original Article


Let Γ be a group generated by a finite set S. We give a sufficient condition for Γ to have Kazhdan's property (T). This condition is easy to check and gives Kazhdan constants. We give examples of groups to which this method applies. We prove that in some setting generic presentations define groups which satisfy this condition and thus have property (T). Moreover we prove that small changes in the presentation of a group satisfying this condition do not change the fact that the group has property (T).


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Copyright information

© Birkhäuser-Verlag 2003

Authors and Affiliations

  1. 1.Unité de Mathématiques Pures et AppliquéesCNRS, Ecole Normale Supérieure de LyonLyon cedex 07France

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