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

Author： Okuyama Takashi  

Publisher： Taylor & Francis Ltd

ISSN： 0092-7872

Source： Communications in Algebra, Vol.30, Iss.12, 2002-01, pp. : 5941-5953

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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.

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