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Journal of the London Mathematical Society 1997 55(3):588-600; doi:10.1112/S0024610797005140
© 1997 by London Mathematical Society
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© The London Mathematical Society

Isoperimetric Inequalities in Nilpotent Groups

Christophe Pittet

Laboratoire de Mathematiques E. Picard, Université Paul Sabatier 118 route de Narbonne, 31062 Toulouse Cedex 4, France. E-mail: pittet{at}picard.ups-tlse.fr

Received 14 April 1994. Revision received 1 May 1995.

To each finitely generated nilpotent group {Gamma}, we associate an integer d and show that the 2-dimensional isoperimetric function (the Dehn function) of {Gamma} is bounded below by a polynomial function of degree d. In the case of free nilpotent groups of class c we find (if we exclude Z) that d=c+1.


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