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On Degrees of Growth of Finitely Generated Groups

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Abstract

We prove that for an arbitrary function ρ of subexponential growth there exists a group G of intermediate growth whose growth function satisfies the inequality v G,S (n) ⩾ ρ(n) for all n. For every prime p, one can take G to be a p-group; one can also take a torsion-free group G. We also discuss some generalizations of this assertion.

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Authors and Affiliations

  1. CNRS, Universite Lille 1, UFR de Mathematiques, France

    A. G. Erschler

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  1. A. G. Erschler
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__________

Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 39, No. 4, pp. 86–89, 2005

Original Russian Text Copyright © by A. G. Erschler

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Erschler, A.G. On Degrees of Growth of Finitely Generated Groups. Funct Anal Its Appl 39, 317–320 (2005). https://doi.org/10.1007/s10688-005-0055-z

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  • DOI: https://doi.org/10.1007/s10688-005-0055-z

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