On exponential growth rates for free groups
type: Item
instance of: scholarly article
title: On exponential growth rates for free groups
zbMATH Open document ID: 0929.20022
DOI: 10.5565/PUBLMAT_42298_13
author: Malik Koubi
published in: Publicacions Matemàtiques
publication date: 1999-11-02T00:00:00Z
full work available at URL: https://eudml.org/doc/41342
review text: It is well known that, with respect to any basis of a free group \(F_n\) of rank \(n\), the exponential growth rate is \(2n-1\). It is shown in the paper that the exponential growth rate of a group \(G\) with respect to an \(n\)-element generating set \(X\) is \(2n-1\) if and only if \(G\) is free on \(X\).
Mathematics Subject Classification ID: 20E05
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20F06
zbMATH DE Number: 1267260
zbMATH Keywords: free groups
zbMATH Keywords: word lengths
zbMATH Keywords: exponential growth rates
zbMATH Keywords: generating sets
zbMATH Keywords: groups of exponential growth
reviewed by: Vitaliĭ Roman'kov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1267260