Amalgamated products and properly 3-realizable groups

Abstract In this paper, we show that the class of all properly 3-realizable groups is closed under amalgamated free products (and HNN-extensions) over finite groups. We recall that G is said to be properly 3-realizable if there exists a compact 2-polyhedron K with π 1 ( K ) ≅ G and whose universal cover K has the proper homotopy type of a 3-manifold (with boundary).