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

  • R. I. Grigorchuk
  • R. Kravchenko


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 $g(n) = \mathrm{l}\mathrm{o}\mathrm{g}(\mathrm{l}\mathrm{o}\mathrm{g}(n))$.
How to Cite
Grigorchuk, R. I., and R. Kravchenko. “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, https://umj.imath.kiev.ua/index.php/umj/article/view/1548.
Research articles