Abstract
Using the group <a,b|a3=b3=(ab)3=1>, we refute the conjecture dubbed in 1976 by V. Belyaev and N. Sesekin, which maintained that the growth function σ(n) of a finitely generated group satisfies the inequality σ(n)≤(σ(n−1)+σ(n+1))/2 for all sufficiently large n.
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Supported by the National Research Foundation of Switzerland, and by RFFR grant No. 96-01-00974.
Translated fromAlgebra i Logika, Vol. 37, No. 6, pp. 621–626, November–December, 1998.
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de la Harpe, P., Grigorchuk, P.I. Local convexity of the growth function of finitely generated groups and question 5.2 in the Kourovka Notebook. Algebr Logic 37, 353–356 (1998). https://doi.org/10.1007/BF02671688
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DOI: https://doi.org/10.1007/BF02671688