5 problems

Let $G$ be a hyperbolic group, and suppose that $G$ has property (LR). Let $H$ be a finite index supergroup of $G$. The commensurability conjecture for hyperbolic groups. The group…

Let $A$ be a finitely generated abelian group and let $G$ be a conjugacy separable group with separable cyclic subgroups. For groups with conjugacy depth function…

Twisted conjugacy separability domination conjecture. For every automorphism $\varphi\in\operatorname{Aut}(N)$,

Conjugacy separability growth conjecture.

Profinite-completion conjecture for conjugacy separability. Conjugacy separability is a property of the profinite completion for residually finite, finitely presented groups.