8 problems

Miller's conjecture. If $G$ is a Miller $p$-group for an odd prime $p$, then $G$ is special.

Let $G$ be a $\det$-finite group, meaning that the relevant Fuglede–Kadison determinants are finite, and let $\Phi\colon G\to G$ be an automorphism. Assume that $G$ has subexponent…

Semicompleteness characterization. The graph product $G_\Gamma$ is semicomplete if and only if $\Gamma$ has no separating star.

Berkovich's conjecture. Every finite nonabelian $p$-group admits a non-inner automorphism of order $p$.

Let $G$ be a virtually cocompact special group. An acylindrically hyperbolic automorphism-group conjecture. If $G$ is acylindrically hyperbolic, then its automorphism group … is ac…

Let $S$ be a surface whose genus is finite and at least $4$. The groups $\operatorname{PMap}(S)$, $\operatorname{Map}(S)$, and $\operatorname{Map}^\pm(S)$ denote the pure mapping c…

Let $G$ be a finitely generated group such that $h_{alg}(id_G)=\infty$, equivalently, $G$ has exponential growth. Infinite algebraic entropy conjecture. Then $h_{alg}(\phi)=\infty$…

Let $A_\Gamma$ be a right-angled Artin group, and let $\Gamma$ be austere, meaning that its defining graph has no nontrivial graph symmetries, no dominated vertices, and no separat…