Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-24T19:57:21.443Z Has data issue: false hasContentIssue false
  • English
  • Français

Primary Groups Whose Basic Subgroup Decompositions can be Lifted

Published online by Cambridge University Press:  20 November 2018

K. Benabdallah  and
A. Laroche
K. Benabdallah
Affiliation:
Département de Mathematique et Statistique Université de Montréal, Canada
A. Laroche
Affiliation:
Department of Mathematics Kuwait University, Kuwait
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.

A primary group G is said to be a l.i.b. group if every idempotent endomorphism of every basic subgroup of G can be extended to an endomorphism of G. We establish the following characterization: A primary group is a l.i.b. group if and only if it is the direct sum of a torsion complete group and a divisible group. The technique used consists of a close analysis of certain subgroups of Prufer-like primary groups.

Keywords

20K10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 1 , 01 March 1984 , pp. 38 - 42
Copyright
Copyright © Canadian Mathematical Society 1984

References

1. Benabdallah, K., Irwin, I. and Rafiq, M., On a core class of Abelian p-groups, Symposia Math. Vol. XIII pp. 195-206 (1972) Rome.Google Scholar
2. Benabdallah, K. and Laroche, A., Quasi-p-pure-injective groups, Can. J. Math. Vol. XXIX No. 3, pp. 578-586 (1977).Google Scholar
3. Fuchs, L., Infinite Abelian Groups, Vol. I Academic Press, New York (1970).Google Scholar
4. Fuchs, L., Infinite Abelian Groups, Vol. II Academic Press, New York (1973).Google Scholar
5. Hill, P. and Meggibben, C.., Quasi-closed primary groups, Acta Math. Acad. Sci. Hungar. 16, pp. 271-274 (1965).Google Scholar
6. Koyama, T. and Irwin, J., On topological methods in Abelian groups, Studies on Abelian groups, pp. 207-222 Dunod, Paris (1968).Google Scholar