Geodesic
A Problem on Relative Projectivity for Abelian Groups
Canadian mathematical bulletin, Tome 29 (1986) no. 1, pp. 114-122

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-1986-021-9
Mots-clés : abelian group, projectivity, module, 13C10, 20K40 
Feigelstock, S.; Raphael, R. A Problem on Relative Projectivity for Abelian Groups. Canadian mathematical bulletin, Tome 29 (1986) no. 1, pp. 114-122. doi: 10.4153/CMB-1986-021-9
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