On iterated torsion products of Abelian \(p\)-groups

DOI10.1216/rmjm/1181072928zbMath0773.20021OpenAlexW2035229563MaRDI QIDQ1206742

Patrick W. Keef

Publication date: 1 April 1993

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmjm/1181072928

zbMATH Keywords

\(p\)-groupsreduced groupsascending chain of subgroups\(\lambda\)-pure subgroupdirect sum of countable groupsiterated torsion productnormal \(\lambda\)-developmentsnormal \(C_ \lambda\) groups

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) Subgroups of abelian groups (20K27)

Related Items (10)

Valuated vector spaces, Kurepa's hypothesis and Abelian \(p\)-groups ⋮ The affinity of set theory and abelian group theory. ⋮ Generalizations of primary Abelian \(C_\alpha\) groups. ⋮ On the torsion product and direct sums of primary cyclic groups. ⋮ On separable \(\widetilde p^\alpha\)-bounded primary Abelian groups. ⋮ An Invariant on Primary Abelian Groups with Applications to Their Projective Dimensions ⋮ Some Isomorphisms of Abelian Groups Involving the Tor Functor ⋮ A theorem on the closure of \(\Omega\)-pure subgroups of \(C_{\Omega}\) groups in the \(\Omega\)-topology ⋮ On elongations of totally projective groups and \(\alpha\)-\(\Sigma\)-groups. ⋮ Classes of Subgroups of Simply Presented Primary Abelian Groups

Cites Work

• When Tor(A,B) is a direct sum of cyclic groups
• The balance of Tor
• On the Tor functor and some classes of Abelian groups
• On singular compactness
• On the structure of Tor. II
• A family of functors defined on generalized primary groups
• Homology and direct sums of countable abelian groups
• Isotype subgroups of direct sums of countable groups
• A generalization of the classical theory of primary groups
• The Recovery of Some Abelian Groups from Their Socles
• The Balanced-Projective Dimension of Abelian p-Groups

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