Displaying similar documents to “An alternative proof of Hill's criterion of freeness for Abelian groups.”

A property of B 2 -groups

Kulumani M. Rangaswamy (1994)

Commentationes Mathematicae Universitatis Carolinae

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It is shown, under ZFC, that a B 2 -group has the interesting property of being ℵ 0 -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 B 2 -groups.

Abelian groups have/are near Frattini subgroups

Simion Breaz, Grigore Călugăreanu (2002)

Commentationes Mathematicae Universitatis Carolinae

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The notions of nearly-maximal and near Frattini subgroups considered by J.B. Riles in [20] and the natural related notions are characterized for abelian groups.

Butler groups and Shelah's Singular Compactness

Ladislav Bican (1996)

Commentationes Mathematicae Universitatis Carolinae

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A torsion-free group is a B 2 -group if and only if it has an axiom-3 family ℭ of decent subgroups such that each member of ℭ has such a family, too. Such a family is called S L ℵ 0 -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 B in a prebalanced and TEP exact sequence 0 → K → C → B → 0 is a B 2 -group provided K and C are so.