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On the Asymptotics of the Growth of 2-Step Nilpotent Groups

Authors:	Stoll Michael

Institution:	Mathematisches Institut der Universität Universitätsstraße 1, D-40225 Düsseldorf, Germany. E-mail: stoll{at}math.uni-duesseldorf.de

Abstract:	Pansu has shown that the growth function of every virtuallynilpotent group ${Gamma}$ with respect to any finite generating set hasasymptotics ${gamma}$ (n) $~$ ${alpha}$ n^d, where d is the degree of growth of ${Gamma}$ . Thepaper refines his result in the special case of 2-step nilpotentgroups to obtain ${gamma}$ (n)= ${alpha}$ n^d+O(n^d–1).

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