Groups whose subgroups have small automizers
type: Item
instance of: scholarly article
title: Groups whose subgroups have small automizers
zbMATH Open document ID: 0921.20043
DOI: 10.1007/BF02844375
author: Rolf Brandl
author: Silvana Franciosi
author: F. de Giovanni
publication date: 1999-10-04T00:00:00Z
review text: A SANS-group was defined by Brandl and the reviewer to be a group \(G\) such that \(N_G(H)=HC_G(H)\) for every nonabelian subgroup \(H\) of \(G\) and the structure of the finite SANS-groups was completely elucidated in a previous paper. In the paper under review, the authors continue the program, initiated by the reviewer, of describing groups via conditions imposed on the automizers of their subgroups. By carefully finding their way through the maze of finiteness conditions and by fully using the available information from the finite case, the authors manage to describe the locally finite non-nilpotent SANS-groups and the locally soluble non-nilpotent SANS-groups.
Mathematics Subject Classification ID: 20F28
Mathematics Subject Classification ID: 20E34
Mathematics Subject Classification ID: 20F50
Mathematics Subject Classification ID: 20E25
Mathematics Subject Classification ID: 20E36
Mathematics Subject Classification ID: 20F19
zbMATH DE Number: 1279147
zbMATH Keywords: locally nilpotent groups
zbMATH Keywords: locally soluble groups
zbMATH Keywords: SANS-groups
zbMATH Keywords: automizers
zbMATH Keywords: subgroups
zbMATH Keywords: finiteness conditions
reviewed by: Marian Deaconescu
MaRDI profile type: Publication
cites work: Finite Groups with Large Automizers for their Abelian Subgroups
cites work: Finite groups with small automizers of their nonabelian subgroups
cites work: Finite groups with large automizers for their nonabelian subgroups
cites work: Endliche Gruppen I
cites work: On a question of Deaconescu about automorphisms
cites work: Finiteness conditions on subnormal and ascendant Abelian subgroups
cites work: Q5654235
cites work: Q3941589
cites work: On a question of Deaconescu about automorphisms. II
cites work: A Group-Theoretic Proof of a Theorem of MacLagan-Wedderburn
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 1279147