An elementary proof of the Benjamini-Nekrashevych-Pete conjecture for the semi-direct products ${\mathbb{Z}}^n⋊\mathbb{Z}$

Dean Wardell

A finitely generated group $G$ is called strongly scale-invariant if there exists an injective homomorphism $f:G\to G$ such that $f(G)$ is a finite index subgroup of $G$ and such t…