Residual properties of graph products of groups

Federico Berlai, Michal Ferov

Published 2015-05-19Version 1

We prove that the class of residually $\mathcal{C}$ groups is closed under taking graph products, provided that $\mathcal{C}$ is closed under taking subgroups, finite direct products and that free-by-$\mathcal{C}$ groups are residually $\mathcal{C}$. As a consequence, we show that local embeddability into various classes of groups is stable under graph products. In particular, we prove that graph products of residually amenable groups are residually amenable, and that locally embeddable into amenable groups are closed under taking graph products.