Groups with normality conditions for subgroups of infinite rank.
type: Item
instance of: scholarly article
title: Groups with normality conditions for subgroups of infinite rank.
zbMATH Open document ID: 1310.20038
DOI: 10.5565/PUBLMAT_58214_16
author: M. De Falco
author: F. de Giovanni
author: C. Musella
published in: Publicacions Matemàtiques
publication date: 2014-08-22T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.pm/1405949321
Mathematics Subject Classification ID: 20F24
Mathematics Subject Classification ID: 20F22
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E15
zbMATH DE Number: 6333798
zbMATH Keywords: almost normal subgroups
zbMATH Keywords: infinite rank subgroups
zbMATH Keywords: nearly normal subgroups
zbMATH Keywords: normal-by-finite subgroups
reviewed by: Martyn Dixon
MaRDI profile type: Publication
OpenAlex ID: W2095534273
review text: A recent theme in infinite group theory is to study groups whose subgroups of infinite rank satisfy some additional property, which is then used to see how this affects the structure of the entire group. This theme is once again taken up very nicely in this paper.NEWLINENEWLINE The authors obtain three main results connected to the properties ``almost normal'', ``nearly normal'', and ``normal-by-finite``. The following result (Theorem B) is typical of the kind obtained: Let \(G\) be a generalized radical group of infinite rank in which every subgroup of infinite rank is nearly normal. Then the commutator subgroup of \(G\) is finite.
description: scientific article; zbMATH DE number 6333798