Geodesic
Pure N-high Subgroups, P-adic Topology and Direct Sums of Cyclic Groups
Canadian journal of mathematics, Tome 26 (1974) no. 2, pp. 322-327

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This paper is divided into two sections. In the first, we characterize the subgroups N of a reduced abelian primary group for which all pure N-high subgroups are bounded. This condition on pure N-high subgroups occurs in several instances, for instance, all pure N-high subgroups of a primary group G are bounded if G is the smallest pure subgroup of G containing N; all N-high subgroups are bounded if N ≠ 0 and all N-high subgroups are closed in the p-adic topology. 
Benabdallah, Khalid; Irwin, John. Pure N-high Subgroups, P-adic Topology and Direct Sums of Cyclic Groups. Canadian journal of mathematics, Tome 26 (1974) no. 2, pp. 322-327. doi: 10.4153/CJM-1974-033-2
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