Geodesic
On Pure-High Subgroups of Abelian Groups
Canadian mathematical bulletin, Tome 17 (1974) no. 4, pp. 479-482

Voir la notice de l'article provenant de la source Cambridge University Press

Fuchs, in [3], problem 14, proposes the study of pure-high subgroups of an abelian group. In this paper we show that in abelian torsion groups, pure-high subgroups are also high. A natural problem arises, that of characterizing the pure-absolute summands. We show that this concept is the same as absolute summands in torsion groups, but that it is more general in mixed abelian groups. There is a definite connection between the existence of pure TV-high subgroups and the splitting of mixed groups. The notation is that of [3]. 
Benabdallah, K. On Pure-High Subgroups of Abelian Groups. Canadian mathematical bulletin, Tome 17 (1974) no. 4, pp. 479-482. doi: 10.4153/CMB-1974-084-3
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[1] 1. Benabdallah, K. and Irwin, J. M., On N-high subgroups of abelian groups', Bull. Soc. Math. France 96, 1968, 337-346. Google Scholar

[2] 2. Fuchs, L., Abelian groups, Budapest, Hungarian academy of science 1958. Google Scholar

[3] 3. Fuchs, L., Infinite Abelian groups, Academic press Mathematics 36-1 New York 1970. Google Scholar

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[5] 5. Kaplansky, I., Infinite Abelian groups, Ann Arbor, University Michigan Press 1954. Google Scholar

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