Quasi-isomorphism invariants for two classes of finite rank Butler groups

Abstract:

A complete set of numerical quasi-isomorphism invariants is given for a class of torsion-free abelian groups containing all groups of the form $\mathcal {G}[\mathcal {A}]$, where $\mathcal {A} = ({A_1}, \ldots ,{A_n})$ is an $n$-tuple of subgroups of the additive rationals and $\mathcal {G}[\mathcal {A}]$ is the cokernel of the diagonal embedding $\bigcap {{A_i} \to \oplus {A_i}}$. This classification and its dual include, as special cases, earlier classifications of strongly indecomposable groups of the form $\mathcal {G}[\mathcal {A}]$ and their duals.