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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
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Abstract

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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

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