5 problems

Let $F$) be Thompson's group, and let $G$ be a subgroup of $F$. A group is elementary amenable if it belongs to the class obtained from finite and abelian groups by transfinite ext…

Finite Hirsch length conjecture. The group $G$ has finite Hirsch length if and only if

Let $G$ be an elementary amenable group acting minimally and essentially freely on an infinite compact metrizable space $X$ with the small boundary property. The action is almost f…

Cohomological-dimension conjecture. The cohomological dimension $\operatorname{cd}_{k}(G)$ is finite if and only if

Let $G$ be an elementary amenable group and let $k$ be a non-zero commutative ring. The homological dimension–Hirsch length conjecture. If $G$ has no $k$-torsion, then … Equivalent…