–HIGH SUBGROUPS OF ABELIAN GROUPS OF TORSION-FREE RANK 1![Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5943/TOC-Subject-Sample-2021-Mathematics-Statistics.jpg"})
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 type
type
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.