Minimal exponential growth rates of metabelian Baumslag-Solitar groups and lamplighter groups

Michelle Bucher, Alexey Talambutsa

We prove that for any prime $p\ge 3$ the minimal exponential growth rate of the Baumslag-Solitar group $BS(1,p)$ and the lamplighter group $\mathcal{L}_p=(\mathbb{Z}/p\mathbb{Z})\…