Most abelian \(p\)-groups are determined by the Jacobson radical of their endomorphism rings
The torsion radical of a ring is the ideal consisting of all torsion elements in its Jacobson radical. It is shown that an abelian \(p\)-group with unbounded basic subgroup is determined by the torsion radical of its endomorphism ring. For \(p\)-groups which are bounded modulo their maximal divisible subgroups, the theorem fails.
scientific article; zbMATH DE number 704928