Grigorchuk group of intermediate growth.
type: Item
instance of: scholarly article
title: Grigorchuk group of intermediate growth.
zbMATH Open document ID: 1142.20308
DOI: 10.1007/BF02843919
author: Antonio Machì
author: Fabio Scarabotti
author: Tullio Ceccherini-Silberstein
publication date: 2008-06-24T00:00:00Z
review text: The authors give an explicit description of the 2-group of intermediate growth introduced by R. I. Grigorchuk and its most significant properties. The existence of this group allowed to give a negative answer to a question of J. Milnor in which he asked if a finitely generated group has necessarily polynomial or exponential growth, that is, if the growth function \(\gamma(n)\) has a pattern of the type \(n^d\) or type \(a^n\), with \(d\in\mathbb{N}^+\), \(a\in(1,+\infty)\). This group furnishes also the first example of a non-elementary amenable group, and thus answers a problem proposed by M. Day. It provides an additional example of a group of Burnside.
Mathematics Subject Classification ID: 20F50
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 43A07
zbMATH DE Number: 5292338
zbMATH Keywords: finitely generated groups
zbMATH Keywords: groups of intermediate growth
zbMATH Keywords: growth functions
reviewed by: C. Pereira da Silva
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02843919
OpenAlex ID: W2050960873
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 5292338