On a class of generalized nilpotent groups
type: Item
instance of: scholarly article
title: On a class of generalized nilpotent groups
zbMATH Open document ID: 0999.20022
author: Tatiana Pedraza
author: Adolfo Ballester-Bolinches
published in: Journal of Algebra
publication date: 2002-07-04T00:00:00Z
review text: The authors work in the class \(A\) (just my notation for this review only) of locally finite groups that are radical (that is, are hyper locally nilpotent) and which satisfy the minimal condition on \(p\)-subgroups for every prime \(p\). Within this class they consider the class \(B\) of all groups \(G\) with the property that every proper subgroup lies in a proper normal subgroup of \(G\). Note that \(A\) is a class of generalized soluble groups and \(B\) is a class of generalized nilpotent groups. The authors' aim is to show that within \(A\) the class \(B\) behaves very much as the class of finite nilpotent groups does within the class of finite soluble groups. In a whole host of ways I think the authors fully succeed with their objective. Of course minor modifications have to be made here and there to allow for the lack of finiteness. Perhaps the most dramatic of these is the replacement of the standard Frattini subgroup by the Frattini-like subgroup introduced by \textit{M. J. Tomkinson} [see Math. Proc. Camb. Philos. Soc 77, 247-257 (1975; Zbl 0301.20018)].
Mathematics Subject Classification ID: 20F19
Mathematics Subject Classification ID: 20F50
zbMATH DE Number: 1763583
zbMATH Keywords: locally finite groups
zbMATH Keywords: minimal condition on \(p\)-subgroups
zbMATH Keywords: generalized soluble groups
zbMATH Keywords: generalized nilpotent groups
zbMATH Keywords: Frattini-like subgroups
reviewed by: B. A. F. Wehrfritz
MaRDI profile type: Publication
full work available at URL: jabr.2001.9035
OpenAlex ID: W2030569064
cites work: A Gaschütz-Lubeseder type theorem in a class of locally finite groups
cites work: Q4856782
cites work: Finite soluble groups
cites work: Q3961021
cites work: Q4177758
cites work: A Frattini-like subgroup
cites work: Q3485064
cites work: Schunck classes and projectors in a class of locally finite groups
DOI: 10.1006/JABR.2001.9035
description: scientific article; zbMATH DE number 1763583