Groups with restrictions on their infinite normal subgroups
type: Item
instance of: scholarly article
title: Groups with restrictions on their infinite normal subgroups
zbMATH Open document ID: 0726.20025
author: F. de Giovanni
published in: Ricerche di Matematica
publication date: 1989-01-01T00:00:00Z
review text: This paper is concerned with classes of groups I\({\mathcal X}\) where \({\mathcal X}\) is the class of finite groups (\({\mathcal F})\) or abelian groups (\({\mathcal A})\) and a group is in I\({\mathcal X}\) if G is not in \({\mathcal X}\), but all quotients of G by an infinite normal subgroup are in \({\mathcal X}\). Radical- by-finite I\({\mathcal F}\) groups are fully characterized and the remaining I\({\mathcal F}\) groups are also described in some detail. Nilpotent I\({\mathcal A}\) groups are shown to exist in a variety of forms, with several characterizations being given. Finally soluble non-nilpotent I\({\mathcal A}\) groups are studied, again with satisfying results. A number of examples and constructions are given. The description of the various classes are not unduly technical.
Mathematics Subject Classification ID: 20F16
Mathematics Subject Classification ID: 20E34
Mathematics Subject Classification ID: 20E36
zbMATH DE Number: 4198321
zbMATH Keywords: just-non-\({\mathcal X}\) groups
zbMATH Keywords: class of finite groups
zbMATH Keywords: infinite normal subgroup
zbMATH Keywords: Radical-by-finite I\({\mathcal F}\) groups
zbMATH Keywords: Nilpotent I\({\mathcal A}\) groups
zbMATH Keywords: soluble non-nilpotent I\({\mathcal A}\) groups
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4198321