publication . Article . Preprint . 2018

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

Rostyslav Kravchenko; Rostislav Grigorchuk;
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  • Published: 22 Feb 2018 Journal: Ukrainian Mathematical Journal, volume 70, pages 182-196 (issn: 0041-5995, eissn: 1573-9376, Copyright policy)
  • Publisher: Springer Science and Business Media LLC
Abstract
We introduce and investigate a rigidity property of rank gradient for an example of a group $$ \mathcal{G} $$ of intermediate growth constructed by the first author in [R. I. Grigorchuk, Funkts.. Anal. Prilozh., 14 No. 1, 53–54 (1980)]. It is shown that $$ \mathcal{G} $$ is normally (f, g)-RG rigid, where f(n) = log(n) and g(n) = log(log(n)).
doi: 10.1007/s11253-018-1494-z
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free text keywords: General Mathematics, Mathematics - Dynamical Systems, Mathematics - Group Theory, Rigidity (psychology), Combinatorics, Mathematics
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