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.
Citation
Yves de Cornulier. "Haagerup Property for subgroups of ${SL}_2$ and residually free groups." Bull. Belg. Math. Soc. Simon Stevin 13 (2) 341 - 343, June 2006. https://doi.org/10.36045/bbms/1148059468
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