A problem about normal subgroups
type: Item
instance of: scholarly article
title: A problem about normal subgroups
zbMATH Open document ID: 0797.20027
DOI: 10.1016/0022-4049(93)90020-T
author: Howard Smith
author: John C. Lennox
author: James Wiegold
published in: Journal of Pure and Applied Algebra
publication date: 1993-11-01T00:00:00Z
review text: The authors prove the following theorem. Suppose \(G\) is a finitely generated group with a proper normal subgroup of finite index. If \(G\) is isomorphic to all of its non-trivial normal subgroups then \(G\) is infinite cyclic. In a particular case this answers a question raised by P. Hall.
Mathematics Subject Classification ID: 20E34
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E36
zbMATH DE Number: 427665
zbMATH Keywords: infinite groups
zbMATH Keywords: finitely generated group
zbMATH Keywords: normal subgroup of finite index
zbMATH Keywords: infinite cyclic
MaRDI profile type: Publication
cites work: Growth sequences of finitely generated groups
full work available at URL: 0022-4049(93)90020-t
OpenAlex ID: W2091729635
description: scientific article; zbMATH DE number 427665