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.
Cite this article
Menny Aka, Profinite completions and Kazhdan’s property (T). Groups Geom. Dyn. 6 (2012), no. 2, pp. 221–229DOI 10.4171/GGD/155