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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

$ G$-projective groups


Authors: C. Vinsonhaler and W. Wickless
Journal: Proc. Amer. Math. Soc. 92 (1984), 164-166
MSC: Primary 20K15; Secondary 20K40
MathSciNet review: 754694
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Abstract: Let TF be the category of torsion free abelian groups of finite rank and homomorphisms. For $ G$ in TF let $ {\text{PC}}\left( G \right)$ be the projective class in TF generated by $ \left\{ G \right\}$. Theorem. $ {\text{PC}}\left( G \right)$ consists exactly of groups of the form $ P \oplus F$, where $ F$ is finite rank free and $ P$ is $ G$-projective $ P \oplus P' \cong {G^n}$ for some positive integer $ n$).


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DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0754694-2
PII: S 0002-9939(1984)0754694-2
Article copyright: © Copyright 1984 American Mathematical Society