4 problems

Let $G$ be a finitely generated group with growth function $\gamma_G(n)$, and let $\beta$ be the parameter used in the stronger form $G^*(\beta)$ of the parameterized Gap Conjectur…

Let $G$ be a finitely generated group with growth function $\gamma_G(n)$, and let $\beta$ satisfy $0<\beta<1$. Weak Gap Conjecture. There exists such a $\beta$ for which … implies…

Let $G$ be a finitely generated group with growth function $\gamma_G(n)$, and let $\beta$ satisfy $0<\beta<1$. Gap Conjecture with parameter $\beta$. If … then $G$ has polynomial g…

Let $G$ be a finitely generated group with growth function $\gamma_G(n)$. Write $f\prec g$ when $f$ is strictly bounded above by $g$ in the relevant growth comparison. Gap Conjectu…