## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Haagerup Property for subgroups of ${SL}_2$ and residually free groups

Yves de Cornulier

#### Abstract

In this note, we prove that all subgroups of $\textnormal{SL}(2,R)$ have the Haagerup Property if $R$ is a commutative reduced ring. This is based on the case when $R$ is a field, recently established by Guentner, Higson, and Weinberger. As an application, residually free groups have the Haagerup Property.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 13, Number 2 (2006), 341-343.

Dates
First available in Project Euclid: 19 May 2006

https://projecteuclid.org/euclid.bbms/1148059468

Digital Object Identifier
doi:10.36045/bbms/1148059468

Mathematical Reviews number (MathSciNet)
MR2259912

Zentralblatt MATH identifier
1141.22002

#### Citation

de Cornulier, Yves. Haagerup Property for subgroups of ${SL}_2$ and residually free groups. Bull. Belg. Math. Soc. Simon Stevin 13 (2006), no. 2, 341--343. doi:10.36045/bbms/1148059468. https://projecteuclid.org/euclid.bbms/1148059468