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Isomorphism invariants for abelian groups


Authors: D. M. Arnold and C. I. Vinsonhaler
Journal: Trans. Amer. Math. Soc. 330 (1992), 711-724
MSC: Primary 20K15
DOI: https://doi.org/10.1090/S0002-9947-1992-1040040-5
MathSciNet review: 1040040
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Abstract: Let $ A= ({A_1},\ldots,{A_n})$ be an $ n$-tuple of subgroups of the additive group, $ Q$, of rational numbers and let $ G(A)$ be the kernel of the summation map $ {A_1} \oplus \cdots \oplus {A_n} \to \sum \;{A_i}$ and $ G[A]$ the cokernel of the diagonal embedding $ \cap \,{A_1} \to {A_1} \oplus \cdots \oplus {A_n}$. A complete set of isomorphism invariants for all strongly indecomposable abelian groups of the form $ G(A)$, respectively, $ G[A]$, is given. These invariants are then extended to complete sets of isomorphism invariants for direct sums of such groups and for a class of mixed abelian groups properly containing the class of Warfield groups.


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DOI: https://doi.org/10.1090/S0002-9947-1992-1040040-5
Article copyright: © Copyright 1992 American Mathematical Society

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