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On Pure-High Subgroups of Abelian Groups

Published online by Cambridge University Press:  20 November 2018

K. Benabdallah
K. Benabdallah*
Affiliation:
Université de Montréal, Montréal, Québec
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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].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 4 , 01 December 1974 , pp. 479 - 482
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Benabdallah, K. and Irwin, J. M., On N-high subgroups of abelian groups', Bull. Soc. Math. France 96, 1968, 337-346.Google Scholar
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5. Kaplansky, I., Infinite Abelian groups, Ann Arbor, University Michigan Press 1954.Google Scholar