A bound for groups of linear growth
type: Item
instance of: scholarly article
title: A bound for groups of linear growth
zbMATH Open document ID: 0584.20025
DOI: 10.1007/BF01189278
author: Wilfried Imrich
author: Norbert Seifter
published in: Archiv der Mathematik
publication date: 1987-01-01T00:00:00Z
review text: Let G be a finitely generated group and let f(n) be the number of elements which can be represented by words of length \(\leq n\) in the generators or their inverses. Suppose G is infinite, \(k>0\), and f(k)-f(k- 1)\(\leq k\). Set \(c=f(k)-f(k-1)\). It is shown that G has a subgroup isomorphic to \({\mathbb{Z}}\) of index \(\leq c\) and that this bound is sharp.
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 3935306
zbMATH Keywords: finitely generated group
zbMATH Keywords: cyclic subgroup of finite index
MaRDI profile type: Publication
cites work: Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
cites work: Q5622446
cites work: Die erste Cohomologiegruppe von Überlagerungen und Homotopie- Eigenschaften dreidimensionaler Mannigfaltigkeiten
cites work: Q5651924
cites work: An effective bound for groups of linear growth
full work available at URL: https://doi.org/10.1007/bf01189278
OpenAlex ID: W1992627633
Recommended article: An effective bound for groups of linear growth
Recommended article: The growth of linear groups
Recommended article: Growth in linear groups.
Recommended article: Characterizing linear groups in terms of growth properties
Recommended article: On uniform exponential growth for linear groups.
Recommended article: Groups Whose Subgroup Growth is Less than Linear
Recommended article: On conjugacy growth of linear groups
Recommended article: Asymptotic growth of finite groups
Recommended article: On groups with linear sci growth.
description: scientific article; zbMATH DE number 3935306