–HIGH SUBGROUPS OF ABELIAN GROUPS OF TORSION-FREE RANK 1

Let be an arbitrary abelian group and the maximal torsion subgroup of . A subgroup of is said to be –high in if is maximal with respect to the property of being disjoint from . First, we show that there exists a –high subgroup of an abelian group of torsion–free rank such that typetype for every –high subgroup of . Next, we characterize the abelian group of torsion–free rank all of whose –high subgroups are isomorphic.