Conjugacy separability of generalized free products of surface groups (Q1368593)

A group \(G\) is called conjugacy separable if whenever \(x,y\in G\) are not conjugate in \(G\) then there is a finite factor group of \(G\) in which the images of \(x\) and \(y\) still are not conjugate. The main result is that the amalgamated free products \(A*_H B\), where \(H\) is cyclic and \(A\), \(B\) are surface groups, are conjugacy separable. Since cocompact Fuchsian groups are finite extensions of surface groups it is conjectured that the result also holds when \(A\), \(B\) are finitely generated Fuchsian groups.