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A Problem on Relative Projectivity for Abelian Groups

Published online by Cambridge University Press:  20 November 2018

S. Feigelstock  and
R. Raphael
S. Feigelstock
Affiliation:
Bar-Ilan UniversityRamat-Gan, Israel
R. Raphael
Affiliation:
Bar-Ilan UniversityRamat-Gan, Israel
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Abstract

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The article studies the class of abelian groups G such that in every direct sum decomposition G = A ⊕ B, A is 5-projective. Such groups are called pds groups and they properly include the quasi-projective groups.

The pds torsion groups are fully determined.

The torsion-free case depends on a lemma that establishes freedom in the non-indecomposable case for several classes of groups. There is evidence suggesting freedom in the general reduced torsion-free case but this is not established and prompts a logical discussion. It is shown, for example, that pds torsion-free groups must be Whitehead if they are not indecomposable, but that there exists Whitehead groups that are not pds if there exist non-free Whitehead groups.

The mixed case is characterized and examples are given.

Keywords

abelian groupprojectivitymodule13C1020K40
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 1 , 01 March 1986 , pp. 114 - 122
Copyright
Copyright © Canadian Mathematical Society 1986

References

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