Isoperimetric functions of nilpotent groups amalgamated along a cyclic subgroup

We show that amalgams of finitely generated torsionfree nilpotent groups of class less than or equal to c along a cyclic subgroup satisfy a polynomial isoperimetric inequality of degree at most 4c(2). The distortion of the am algamated subgroup is bounded above by a polynomial of degree c. We also gi ve an example of a non-cyclic amalgam of finitely generated torsionfree nil potent groups along an abelian, isolated and normal subgroup having an expo nential isoperimetric inequality.