Abstract
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).
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Żuk, A. Property (T) and Kazhdan constants for discrete groups. Geom. funct. anal. 13, 643–670 (2003). https://doi.org/10.1007/s00039-003-0425-8
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s00039-003-0425-8