The embedding of certain linear and Abelian groups in finitely presented simple groups
type: Item
instance of: scholarly article
title: The embedding of certain linear and Abelian groups in finitely presented simple groups
zbMATH Open document ID: 0544.20028
DOI: 10.1016/0021-8693(84)90173-X
author: E. Scott
published in: Journal of Algebra
publication date: 1984-01-01T00:00:00Z
review text: This paper continues the previous one [reviewed above] and applies the results there to embed some groups in finitely presented simple groups. \textit{G. Higman} [in ''Finitely presented simple groups'', Notes on Pure Mathematics 8, The Australian National University Canberra (1974)], showed that any countable locally finite group can be embedded in a finitely presented simple group. The author extends this to show that any linear group over the integers and any countable abelian group where the quotient by the torsion subgroup is a subgroup of a free Z[1/n]-module for some integer n, can be embedded in a finitely presented simple group. This gives some new results, for GL(3,Z) could not be embedded in any of the previously known finitely presented simple groups. The methods used are very similar to those of the previous paper and this should be read in conjunction with that paper.
Mathematics Subject Classification ID: 20E32
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20F10
zbMATH DE Number: 3865566
zbMATH Keywords: embedding groups
zbMATH Keywords: finitely presented simple groups
zbMATH Keywords: countable locally finite group
reviewed by: J. R. J. Groves
MaRDI profile type: Publication
cites work: Q5609457
cites work: Subgroups of finitely presented groups
cites work: A construction which can be used to produce finitely presented infinite simple groups
description: scientific article; zbMATH DE number 3865566