Groups, Geometry, and Dynamics
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Profinite completions and Kazhdan’s property (T)
Menny Aka (1)(1) Institute of Mathematics, The Hebrew University of Jerusalem, Givat Ram, 91904, JERUSALEM, ISRAEL
We show that property (T) is not profinite, that is, we construct two finitely generated residually finite groups which have isomorphic profinite completions, while one admits property (T) and the other does not. This settles a question raised by M. Kassabov.
Keywords: Profinite groups, profinite properties, Kazhdan’s property (T), arithmetic groups