Geometric & Functional Analysis GAFA

, Volume 13, Issue 3, pp 643–670

Property (T) and Kazhdan constants for discrete groups


    • Unité de Mathématiques Pures et AppliquéesCNRS, Ecole Normale Supérieure de Lyon
Original Article

DOI: 10.1007/s00039-003-0425-8

Cite this article as:
Żuk, A. Geom. funct. anal. (2003) 13: 643. doi:10.1007/s00039-003-0425-8


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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© Birkhäuser-Verlag 2003