On automorphisms fixing infinite subgroups of groups
type: Item
instance of: scholarly article
title: On automorphisms fixing infinite subgroups of groups
zbMATH Open document ID: 0664.20018
DOI: 10.1007/BF01190661
published in: Archiv der Mathematik
publication date: 1990-01-01T00:00:00Z
review text: An automorphism of a group G is said to be a power automorphism if it maps every subgroup of G onto itself. The set PAut G of all power automorphisms of G is an abelian normal subgroup of the full automorphism group Aut G, whose properties were investigated by \textit{C. Cooper} [Math. Z. 107, 335-356 (1968; Zbl 0169.338)]. This paper deals with the structure of the group IAut G of all automorphisms of G leaving every infinite subgroup of G invariant (I-automorphisms). It is shown that, if the group G either is non-periodic or does not involve any infinite simple group, then IAut G is an abelian group. Moreover, when G is a (locally radical)-by-finite group which is not artinian, the groups IAut G and PAut G coincide. In the last part of the paper the structure of the group of I-automorphisms of a nilpotent p-group is investigated.
Mathematics Subject Classification ID: 20F28
Mathematics Subject Classification ID: 20E36
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20F18
Mathematics Subject Classification ID: 20F50
zbMATH DE Number: 4085896
zbMATH Keywords: power automorphisms
zbMATH Keywords: abelian normal subgroup
zbMATH Keywords: full automorphism group
zbMATH Keywords: I- automorphism
zbMATH Keywords: nilpotent p-group
author: Mario Curzio
author: Silvana Franciosi
author: F. de Giovanni
MaRDI profile type: Publication
cites work: Locally finite groups with Chernikov Sylow p-subgroups
cites work: Power automorphisms of a group
cites work: Q5675882
cites work: Q5654235
cites work: Q4083615
description: scientific article; zbMATH DE number 4085896