The existence of certain pure dense subgroups of Abelian p-groups is not decidable in ZFC

DOI10.1016/0021-8693(89)90252-4zbMath0684.20039OpenAlexW2041525432MaRDI QIDQ1825285

Doyle Cutler

Publication date: 1989

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(89)90252-4

zbMATH Keywords

Martin's axiomhigh subgroupsconstructible universe\(V=L\)separable abelian p-groupundecidable in ZFCregular uncountable cardinal\(p^{\omega +n}\)-projective p-groupsdetermined by the \(p^ n\)-socleDirect sums of cyclic groupspure dense subgrouptorsion-complete group

Mathematics Subject Classification ID

Consistency and independence results (03E35) Continuum hypothesis and Martin's axiom (03E50) Torsion groups, primary groups and generalized primary groups (20K10) Subgroups of abelian groups (20K27)

Related Items (2)

Separable Abelian \(p\)-groups having certain prescribed chains ⋮ Abelian groups

Cites Work

• High subgroups of Abelian torsion groups
• On \(N\)-high subgroups of Abelian groups
• High subgroups of primary Abelian groups of length \(\omega +n\)
• Crawley's problem on the unique \(\omega\)-elongation of p-groups is undecidable
• The number of separable _p-groups of cardinality r₁ Having isometric socles
• Primary Abelian Groups Having all High Subgroups Isomorphic
• On Primary Groups with Countable Basic Subgroups
• Summands of Separable Abelian Groups: Dedicated to Paul Turán on his 60th Birthday
• Minimal pure subgroups in primary groups
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