Abstract
The subgroup [Formula: see text] is absolute direct summand (ADS) if, for every [Formula: see text]-high subgroup [Formula: see text] (i.e. maximal with respect to the property [Formula: see text]), we have [Formula: see text], and [Formula: see text] itself is an ADS group if all of its summands inherit this property. In this paper, we characterize the structure of ADS abelian groups, which can be defined as groups such that members of the decomposition into two direct summands are mutually injective. In particular, an ADS abelian group is either divisible, or a direct sum of an indecomposable torsion-free group and a divisible torsion group, or a torsion group such that each [Formula: see text]-component is a direct sum of cyclic [Formula: see text]-groups of the same length or of Prüfer groups.
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