Isomorphism invariants for abelian groups

Arnold, D. M.; Vinsonhaler, C. I.

doi:10.1090/S0002-9947-1992-1040040-5

Isomorphism invariants for abelian groups
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by D. M. Arnold and C. I. Vinsonhaler

Trans. Amer. Math. Soc. 330 (1992), 711-724

DOI: https://doi.org/10.1090/S0002-9947-1992-1040040-5

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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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Isomorphism invariants for abelian groups
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Abstract: