On the rigidity of rank gradient in a group of intermediate growth

  • R. I. Grigorchuk
  • R. Kravchenko

Abstract

We introduce and investigate a rigidity property of rank gradient for an example of a group $\scr G$ of intermediate growth constructed by the first author in [Grigorcuk R. I. On Burnside’s problem on periodic groups // Funktsional. Anal. i Prilozhen. – 1980. – 14, № 1. – P. 53 – 54]. It is shown that $\scr G$ is normally $(f, g)$-RG rigid, where$ f(n) = \mathrm{l}\mathrm{o}\mathrm{g}(n)$ and $g(n) = \mathrm{l}\mathrm{o}\mathrm{g}(\mathrm{l}\mathrm{o}\mathrm{g}(n))$.
Published
25.02.2018
How to Cite
GrigorchukR. I., and KravchenkoR. “On the Rigidity of Rank Gradient in a Group of Intermediate Growth”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, no. 2, Feb. 2018, pp. 165-76, http://umj.imath.kiev.ua/index.php/umj/article/view/1548.
Section
Research articles