A complete set of numerical quasi-isomorphism invariants is given for a class of torsion-free abelian groups containing all groups of the form
G
[
A
]
\mathcal {G}[\mathcal {A}]
, where
A
=
(
A
1
,
…
,
A
n
)
\mathcal {A} = ({A_1}, \ldots ,{A_n})
is an
n
n
-tuple of subgroups of the additive rationals and
G
[
A
]
\mathcal {G}[\mathcal {A}]
is the cokernel of the diagonal embedding
⋂
A
i
→
⊕
A
i
\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
G
[
A
]
\mathcal {G}[\mathcal {A}]
and their duals.