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.
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.
Page 1