5 problems

Let $G$ be a limit group, and let $H$ be a finite index supergroup of $G$. The limit-group supergroup conjecture. The group $H$ has property (LR). This is motivated by Wilton's the…

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.