Abstract
Let H and Γ be two discrete groups and X be a set on which Γ acts. We investigate when the wreath product H≀XΓ has relative property (T) and give a complete characterization of property (T) for such groups. Moreover we determine a lower bound of a Kazhdan constant for H≀XΓ in terms of those for H and Γ. Property (τ) of H≀XΓ is also discussed in some instances.
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