Proving a group infinite
type: Item
instance of: scholarly article
title: Proving a group infinite
zbMATH Open document ID: 0662.20023
DOI: 10.1007/BF01188513
author: M. F. Newman
published in: Archiv der Mathematik
publication date: 1990-01-01T00:00:00Z
review text: A method for proving groups infinite is described. It is based on a version of the Golod-Shafarevich theorem proved by \textit{W. Gaschütz} and \textit{M. F. Newman} [J. Reine Angew. Math. 245, 172-176 (1970; Zbl 0221.20023)]. The method is used to show that ``the last of the Fibonacci groups'' is infinite: this group is generated by \(\{a_ 1,...,a_ 9\}\) subject to defining relations \(a_ 1a_ 2=a_ 3,...,a_ 9a_ 1=a_ 2\); see a paper by \textit{G. Havas}, \textit{J. S. Richardson}, \textit{L. S. Sterling} [Proc. R. Soc. Edinb., Sect. A 83, 199-203 (1979; Zbl 0416.20026)] for an earlier discussion of this group. The information needed to apply the criterion for infiniteness was extracted from the presentation with the aid of a computer using the system SPAS created at Lehrstuhl D für Mathematik in Aachen.
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20-04
zbMATH DE Number: 4081824
zbMATH Keywords: nilpotent quotient
zbMATH Keywords: Golod-Shafarevich theorem
zbMATH Keywords: Fibonacci groups
zbMATH Keywords: relations
zbMATH Keywords: criterion for infiniteness
zbMATH Keywords: computer
zbMATH Keywords: SPAS
MaRDI profile type: Publication
cites work: On presentations of finite p-groups.
cites work: The last of the Fibonacci groups
cites work: Q3877854
cites work: The Fibonacci Groups
full work available at URL: https://doi.org/10.1007/bf01188513
OpenAlex ID: W2007920518
Recommended article: Q4273697
Recommended article: Proving Another Group Infinite
Recommended article: Induction theorems for infinite groups
Recommended article: Q4288965
Recommended article: Q3202286
Recommended article: Infiniteness of a certain group defined by a presentation
Recommended article: On infinite groups
Recommended article: On some infinite groups
Recommended article: A Ramsey statement for infinite groups
description: scientific article; zbMATH DE number 4081824