On the permanence properties of residually exact groups

Abstract

A discrete group $\Gamma$ is called exact if the reduced group C*-algebra ${C_{\lambda}}^{*}(\Gamma)$ is exact as C*-algebras, and a discrete group $\Lambda$ is called residually exact if every nonunital element $g \in \Lambda$ admits a surjective group homomorphism from $\Lambda$ to some exact group $\Gamma$ which maps $g$ to a nonunital element of $\Gamma$. We prove the class of residually exact groups is closed under taking Green's graph products [1], double amalgamed products and special HNN extensions.