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The Quarterly Journal of Mathematics 2001 52(1):33-44; doi:10.1093/qjmath/52.1.33
© 2001 by Oxford University Press
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Isoperimetric functions of nilpotent groups amalgamated along a cyclic subgroup

Christian Hidber1

1 Nussbaumstasse 12, CH-8003, Zurich, Switzerland, e-mail: hidber{at}yahoo.com

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.

Received 28 January 2000.


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