In this note we present a complete set of quasi-isomorphism invariants for strongly indecomposable abelian groups of the form
G
=
G
(
A
1
,
…
,
A
n
)
G = G({A_1}, \ldots ,{A_n})
. Here
A
1
,
…
,
A
n
{A_1}, \ldots ,{A_n}
are subgroups of the rationals
Q
Q
and
G
G
is the kernel of
f
:
A
1
⊕
⋯
⊕
A
n
→
Q
f:{A_1} \oplus \cdots \oplus {A_n} \to Q
, where
f
(
a
1
,
…
,
a
n
)
=
Σ
a
i
f({a_1}, \ldots ,{a_n}) = \Sigma {a_i}
. The invariants are the collection of numbers
rank
∩
{
G
[
σ
]
|
σ
∈
M
}
{\text {rank}} \cap \{ G[\sigma ]|\sigma \in M\}
, where
M
M
ranges over all subsets of the type lattice generated by
{
type
(
A
i
)
}
\left \{ {{\text {type}}({A_i})} \right \}
. Our results generalize the classical result of Baer for finite rank completely decomposable groups, as well as a result of F. Richman on a subset of the groups of the form
G
(
A
1
,
…
,
A
n
)
G({A_1}, \ldots ,{A_n})
.