On some variants of theorems of Schur and Baer.
type: Item
instance of: scholarly article
title: On some variants of theorems of Schur and Baer.
zbMATH Open document ID: 1322.20027
author: Martyn Dixon
author: A. A. Pypka
author: L. A. Kurdachenko
published in: Milan Journal of Mathematics
publication date: 2014-11-27T00:00:00Z
review text: In this interesting paper, the authors continue their efforts to expand a well-known theorem of I. Schur which states that if \(G\) is a group and \(G/\zeta(G)\) is finite then \(G'\) is finite. They obtain an analogue of this result and also of theorems of R. Baer and P. Hall for groups \(G\) that have subgroups \(A\) of \(\Aut(G)\) such that \(A/\mathrm{Inn}(G)\) is finite.
Mathematics Subject Classification ID: 20F14
Mathematics Subject Classification ID: 20F28
zbMATH DE Number: 6374530
zbMATH Keywords: central factor group
zbMATH Keywords: automorphisms
zbMATH Keywords: hypercentre
zbMATH Keywords: Schur theorem
zbMATH Keywords: Baer theorem
zbMATH Keywords: upper central series
zbMATH Keywords: lower central series
reviewed by: Igor Subbotin
MaRDI profile type: Publication
full work available at URL: s00032-014-0215-9
OpenAlex ID: W2017346910
cites work: Endlichkeitskriterien für Kommutatorgruppen
cites work: On the upper central series of infinite groups
cites work: Q3235830
cites work: Torsion-free groups having finite automorphism groups. I
cites work: Groups of exponent 4 as automorphism groups
cites work: Finite groups of exponent 4 as automorphism groups. II
cites work: Finite groups of exponent 12 as automorphism groups
cites work: The absolute centre of a group
cites work: Finite Automorphism Groups of Torsion-Free Groups
cites work: On a generalization of Baer theorem.
cites work: Q5654236
cites work: Multiplicators and groups with finite central factor-groups
DOI: 10.1007/S00032-014-0215-9
description: scientific article; zbMATH DE number 6374530