Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-27T10:18:15.320Z Has data issue: false hasContentIssue false
  • English
  • Français

Sur les Sous-Groupes Purifiables des Groupes Abéliens Primaires

Published online by Cambridge University Press:  20 November 2018

K. Benabdallah  and
C. Piché
K. Benabdallah
Affiliation:
Département de mathématiques et de statistique, Université de Montréal, Montréal, Québec, Canada
C. Piché
Affiliation:
Department of Mathematics, University of Hawaii at Manoa, 2565 The Mall, Honolulu, HI 96822
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The class of primary abelian groups whose subsocles are purifiable is not yet completely characterized and it contains the class of direct sums of cyclic groups and torsion complete groups. In sharp constrast with this, the class of groups whose p2-bounded subgroups are purifiable consist only of those groups which are the direct sum of a bounded and a divisible group. Various tools are developed and a short application to the pure envelopes of cyclic subgroups is given in the last section.

Keywords

20K10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 1 , 01 March 1990 , pp. 11 - 17
Copyright
Copyright © Canadian Mathematical Society 1990

References

Bibliographie

1. Benabdallah, K. and Irwin, J., On minimal pure subgroups, Publ. Math., vol 23, 1976, pp. 111–114.Google Scholar
2. Charles, B., Etudes sur les sous-groupes d'un groupe abélien, Bull. Soc. Math. France, vol 88, 1960, pp. 217–227.Google Scholar
3. Fuchs, L., Infinite Abelian Groups, vol I-II, Academic Press, Inc., London, New York.Google Scholar
4. Hill, P. et Megibben, C., Minimal pure subgroups in primary groups, Bull. Soc. Math. France, vol 92, 1964, pp. 251–257.Google Scholar