Addendum to: “On extensions of fundamental groups of surfaces and related groups”

THEOREM. Let gf be the fundamental group of a surface S and let g be finitely generated. Let © be a group which contains $ as a normal subgroup of finite index and which has the following properties: (i) For each g G © the automorphism of g defined by x\-^g~xg is induced by a homeomorphism of S. (ii) If g e © and g~*xg=x holds for all x G g, then g G g. (iii) If x=y=(xy)=l holds for x,y G© and a, b, c^2, then x, y generate a cyclic subgroup of®. Then © is isomorphic to a finitely generated discontinuous group of motions of the hyperbolic or euclidean plane.