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

 

Invariants for a class of torsion-free abelian groups


Authors: D. Arnold and C. Vinsonhaler
Journal: Proc. Amer. Math. Soc. 105 (1989), 293-300
MSC: Primary 20K15
MathSciNet review: 935102
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Abstract: In this note we present a complete set of quasi-isomorphism invariants for strongly indecomposable abelian groups of the form $ G = G({A_1}, \ldots ,{A_n})$. Here $ {A_1}, \ldots ,{A_n}$ are subgroups of the rationals $ Q$ and $ G$ is the kernel of $ f:{A_1} \oplus \cdots \oplus {A_n} \to Q$, where $ f({a_1}, \ldots ,{a_n}) = \Sigma {a_i}$. The invariants are the collection of numbers $ {\text{rank}} \cap \{ G[\sigma ]\vert\sigma \in M\} $, where $ M$ ranges over all subsets of the type lattice generated by $ \left\{ {{\text{type}}({A_i})} \right\}$. Our results generalize the classical result of Baer for finite rank completely decomposable groups, as well as a result of F. Richman on a subset of the groups of the form $ G({A_1}, \ldots ,{A_n})$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0935102-X
PII: S 0002-9939(1989)0935102-X
Article copyright: © Copyright 1989 American Mathematical Society