Isoperimetric functions of nilpotent groups amalgamated along a cyclic subgroup

Abstract

We show that amalgams of finitely generated torsionfree nilpotent groups of class≤c along a cyclic subgroup satisfy a polynomial isoperimetric inequality of degree at most 4c2. The distortion of the amalgamated subgroup is bounded above by a polynomial of degree c.We also give an example of a non‐cyclic amalgam of finitely generated torsionfree nilpotent groups along an abelian, isolated and normal subgroup having an exponential isoperimetric inequality.