ABSTRACT
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.
ACKNOWLEDGMENT
This work was completed during the author's visit at the University of Hawaii. The author thanks the Department of Mathematics at the University of Hawaii and Professor Adolf Mader for their hospitality. Finally, the author is grateful to Toba National College of Maritime Technology for supporting him during his visit in Hawaii.