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N-pure-high subgroups of Abelian groups. (English) Zbl 0594.20050

Let N be a subgroup of an abelian group G. A subgroup H of G is N-high if H is maximal with respect to \(N\cap H=0\), and N-pure-high if H is pure and maximal with respect to purity and \(N\cap H=0\). It is well known that the distinction between these concepts is useful only if G is mixed. For mixed G, the author studies conditions under which the concepts coincide and derives several properties of N-pure-high subgroups. For example, he shows that the torsion subgroup \(H_ t\) of an N-pure-high subgroup H is \(N_ t\)-pure-high in \(G_ t\), and he gives a useful characterization of the intersection of all N-high and N-pure-high subgroups of G.
Reviewer: P.Schultz

MSC:

20K21 Mixed groups
20K27 Subgroups of abelian groups
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