Another result about non-uniqueness of direct sum decompositions is due to A.L.S. Corner: given integers formula_6, there exists a torsion-free abelian group "A" of rank "n" such that for any partition formula_7 into "k" natural summands, the group "A" is the direct sum of "k" indecomposable subgroups of ranks formula_8. Thus the sequence of ranks of indecomposable summands in a certain direct sum decomposition of a torsion-free abelian group of finite rank is very far from being an invariant of "A".