On the rigidity of rank gradient in a group of intermediate growth

Abstract

We introduce and investigate the rigidity property of rank gradient in the case of the group $\mathcal{G}$ of intermediate growth constructed by the first author. We show that $\mathcal{G}$ is normally $(f,g)$-RG rigid where $f(n)=\log (n)$ and $g(n)=\log (\log (n)).$