, Volume 39, Issue 4, pp 317-320

On Degrees of Growth of Finitely Generated Groups

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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.

Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 39, No. 4, pp. 86–89, 2005
Original Russian Text Copyright © by A. G. Erschler