2019
Том 71
№ 2

# Kravchenko R.

Articles: 2
Article (English)

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

Ukr. Mat. Zh. - 2018. - 70, № 2. - pp. 165-176

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 $g(n) = \mathrm{l}\mathrm{o}\mathrm{g}(\mathrm{l}\mathrm{o}\mathrm{g}(n))$.

Article (English)

### Schreier Graphs for a Self-Similar Action of the Heisenberg Group

Ukr. Mat. Zh. - 2013. - 65, № 11. - pp. 1456–1462

We construct a faithful self-similar action of the discrete Heisenberg group with the following properties: This action is self-replicating, finite-state, level-transitive, and noncontracting. Moreover, there exist orbital Schreier graphs of action on the boundary of the tree with different degrees of growth.