A Class of Primary Abelian Groups Characterized by Its Socles

DOI10.2307/2159210zbMath0774.20032OpenAlexW4230912411MaRDI QIDQ4013474

Patrick W. Keef

Publication date: 27 September 1992

Full work available at URL: https://doi.org/10.2307/2159210

zbMATH Keywords

direct sumstorsion subgroupdirect productabelian \(p\)-groupsisometric soclesvaluated vector spacestorsion-complete groupsclass of groups\(t\)-product

Mathematics Subject Classification ID

Homological and categorical methods for abelian groups (20K40) Torsion groups, primary groups and generalized primary groups (20K10) Direct sums, direct products, etc. for abelian groups (20K25)

Related Items (2)

Classes of primary abelian groups determined by valuated subgroups ⋮ Isomorphism of modular group algebras of direct sums of torsion-complete Abelian \(p\)-groups

Cites Work

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• On socles of Abelian p-groups in L
• A Boolean power and a direct product of Abelian groups
• On reconstructing separable reduced p-groups with a given socle
• On products of primary abelian groups
• Vector spaces with valuations
• On direct sums and products of modules
• Determinimg abelianp-groups from theirn-Socles
• On p^ω+1 -Projective p -Groups
• A classification of direct sums of closed groups
• On Primary Groups with Countable Basic Subgroups
• The Isomorphic Refinement Theorem for Direct Sums of Closed Groups
• On Direct Products of Abelian Groups
• Countable Torsion Products of Abelian p-Groups

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