Subgroup conjugacy separability for surface groups
  A group $G$ is called subgroup conjugacy separable (abbreviated as SCS), if any two finitely generated and non-conjugate subgroups of $G$ remain non-conjugate in some finite quotient of $G$. We prove that free groups and the fundamental groups of orientable closed compact surfaces are SCS. 
Oleg Bogopolski and Kai-Uwe Bux
math.GR