Completely decomposable pure subgroups of completely decomposable abelian groups
L. Fuchs, G. Viljoen (1994)
Rendiconti del Seminario Matematico della Università di Padova
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L. Fuchs, G. Viljoen (1994)
Rendiconti del Seminario Matematico della Università di Padova
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Kulumani M. Rangaswamy (1994)
Commentationes Mathematicae Universitatis Carolinae
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It is shown, under ZFC, that a -group has the interesting property of being -prebalanced in every torsion-free abelian group in which it is a pure subgroup. As a consequence, we obtain alternate proofs of some well-known theorems on -groups.
Ladislav Bican (1996)
Commentationes Mathematicae Universitatis Carolinae
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A torsion-free group is a -group if and only if it has an axiom-3 family of decent subgroups such that each member of has such a family, too. Such a family is called -family. Further, a version of Shelah’s Singular Compactness having a rather simple proof is presented. As a consequence, a short proof of a result [R1] stating that a torsion-free group in a prebalanced and TEP exact sequence is a -group provided and are so.
L. Bican, L. Salce, J. Štěpán (1985)
Rendiconti del Seminario Matematico della Università di Padova
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