A finitely generated group $\Gamma$ is called strongly scale-invariant if there exists an injective endomorphism $\varphi: \Gamma \to \Gamma$ with the image $\varphi(\Gamma)$ of finite index in and subgroup $\bigcap\_{n>0}\varphi^n(\Gamma)$ finite. The only known examples such groups are virtually nilpotent, or equivalently, all have polynomial growth. question by Nekrashevych Pete asks whether...
