The absolute centre of a group
type: Item
instance of: scholarly article
title: The absolute centre of a group
zbMATH Open document ID: 0817.20037
published in: Journal of Algebra
publication date: 1995-08-07T00:00:00Z
review text: The absolute centre of a group \(G\) is the subgroup \(L(G)\) of all elements of \(G\) which are fixed by every automorphism of \(G\), and the auto-commutator subgroup of \(G\) is the subgroup \(G^*\) generated by all products \(g^{-1}g^\alpha\), where \(g\) is in \(G\) and \(\alpha\) is any automorphism of \(G\). The author proves that if \(G/L(G)\) is finite, then also \(G^*\) and \(\Aut\,G\) are finite. He also gives bounds for the orders of \(G^*\) and \(\Aut\,G\) in terms of the order of \(G/L(G)\).
reviewed by: Silvana Franciosi
Mathematics Subject Classification ID: 20E36
Mathematics Subject Classification ID: 20F14
Mathematics Subject Classification ID: 20E34
zbMATH DE Number: 701286
zbMATH Keywords: absolute centre
zbMATH Keywords: automorphisms
zbMATH Keywords: auto-commutator subgroup
author: Peter Hegarty
MaRDI profile type: Publication
full work available at URL: jabr.1994.1318
OpenAlex ID: W2018106980
DOI: 10.1006/JABR.1994.1318
description: scientific article; zbMATH DE number 701286