Profinite completions and Kazhdan’s property (T)

Aka , Menny

doi:10.4171/GGD/155

Groups, Geometry, and Dynamics

Full-Text PDF (131 KB) |

Table of Contents |

GGD summary

Volume 6, Issue 2, 2012, pp. 221–229

DOI: 10.4171/GGD/155

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