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A property of B 2 -groups

Kulumani M. Rangaswamy — 1994

Commentationes Mathematicae Universitatis Carolinae

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

A Note on Countable Butler Groups

David M. ArnoldKulumani M. Rangaswamy — 2007

Bollettino dell'Unione Matematica Italiana

An example of a countable Butler group that is not a pure subgroup of a completely decomposable group was published in 1986. Recently, an error in the proof was discovered. This note includes a corrected argument, as well as a proof that this group has no pure precobalanced subgroups of rank one.

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