A finitely generated simple group with free 2-generated subgroups
type: Item
instance of: scholarly article
title: A finitely generated simple group with free 2-generated subgroups
zbMATH Open document ID: 0616.20013
DOI: 10.1007/BF00969195
published in: Siberian Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: A finitely generated simple group is constructed such that every 2- generated subgroup is free. Thus there exists an infinite finitely generated simple group requiring more than two generators, this answers a question of \textit{J. Wiegold} [The Kourovka Notebook, Transl., II. Ser., Am. Math. Soc. 121 (1983; Zbl 0512.20001), Problem 6.44]. In this construction, the diagram method is used, i.e. a geometrical interpretation of equality of words to the identity element over a given group presentation.
Mathematics Subject Classification ID: 20E32
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 3998078
zbMATH Keywords: finitely generated simple group
zbMATH Keywords: 2-generated subgroup
zbMATH Keywords: generators
zbMATH Keywords: diagram method
zbMATH Keywords: presentation
author: Victor S. Guba
reviewed by: Ju. I. Merzljakov
MaRDI profile type: Publication
cites work: Q3333233
description: scientific article; zbMATH DE number 3998078