Determining Abelian \(p\)-groups by the Jacobson radical of their endomorphism rings
type: Item
instance of: scholarly article
title: Determining Abelian \(p\)-groups by the Jacobson radical of their endomorphism rings
zbMATH Open document ID: 0837.20067
author: Jutta Hausen
author: Johnny A. Johnson
published in: Journal of Algebra
publication date: 1996-04-16T00:00:00Z
review text: A well known result of Baer-Kaplansky on isomorphisms of endomorphism rings \(E(G)\) of abelian \(p\)-groups \(G\) is continued by a study of the Jacobson radical \(J(G)\) of \(E(G)\). The main result of the paper states that every (ring) isomorphism \(J(G)\approx J(G')\) is induced by an isomorphism \(G\approx G'\) iff \(G\) modulo its divisible part is zero or unbounded (for \(p\neq 2)\). There is a similar result describing groups \(G\) such that all automorphisms of \(J(G)\) are induced by automorphisms of \(G\).
Mathematics Subject Classification ID: 20K10
Mathematics Subject Classification ID: 16N20
Mathematics Subject Classification ID: 20K30
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16W20
zbMATH DE Number: 783862
zbMATH Keywords: endomorphism rings
zbMATH Keywords: Abelian \(p\)-groups
zbMATH Keywords: Jacobson radical
zbMATH Keywords: induced by automorphisms
reviewed by: Stanisław Balcerzyk
MaRDI profile type: Publication
full work available at URL: jabr.1995.1125
OpenAlex ID: W2028920338
DOI: 10.1006/JABR.1995.1125
description: scientific article; zbMATH DE number 783862