Isomorphism invariants for abelian groups

Let $A=(A_1,\dots ,A_n)$ 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.