2 problems

Finite-height subgroup conjecture. If $H$ has finite height in $G$, then $H$ is quasi-convex in $G$.

Let $G$ be a group hyperbolic relative to the peripheral system $\mathcal{P}=\{P_1,\ldots,P_n\}$. Suppose that hyperbolic groups are residually finite, and that each $P_i$ is finit…