Determining Abelian \(p\)-groups by the Jacobson radical of their endomorphism rings
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 \(G\).
scientific article; zbMATH DE number 783862