Most abelian \(p\)-groups are determined by the Jacobson radical of their endomorphism rings

DOI10.1007/BF02572332zbMath0811.20046OpenAlexW2058057634WikidataQ56988281 ScholiaQ56988281MaRDI QIDQ1340936

Phillip Schultz, Cheryl E. Praeger, Jutta Hausen

Publication date: 21 December 1994

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/174661

zbMATH Keywords

Jacobson radical\(p\)-groupsendomorphism ringtorsion elementstorsion radicalmaximal divisible subgroupsunbounded basic subgroup

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups (20K30) Torsion groups, primary groups and generalized primary groups (20K10) Jacobson radical, quasimultiplication (16N20) Subgroups of abelian groups (20K27)

Related Items

Unnamed Item, Influence of the Baer-Kaplansky theorem on the development of the theory of groups, rings, and modules, The Jacobson Radical’s Role in Isomorphism Theorems for p-Adic Modules Extends to Topological Isomorphism, Modules over discrete valuation domains. III, Modules over discrete valuation domains. I, A Baer-Kaplansky theorem for modules over principal ideal domains, Around the Baer-Kaplansky theorem, Modules over discrete valuation domains. II, Jacobson Radical Isomorphism Theorems for Mixed Modules Part One: Determining the Torsion

Cites Work

• Unnamed Item
• Quasi-regular ideals of some endomorphism rings
• Characterization of the primary abelian groups, bounded modulo the divisible subgroup, by the radical of their endomorphism rings
• Primary abelian groups as modules over their endomorphism rings
• Automorphism rings of primary abelian operator groups
• On the Jacobson Radical of Some Endomorphism Rings
• Some Results on Abelian Groups