Direct sums of local torsion-free abelian groups

The category of local torsion-free abelian groups of finite rank is known to have the cancellation and $n$ -th root properties but not the Krull-Schmidt property. It is shown that 10 is the least rank of a local torsion-free abelian group with two non-equivalent direct sum decompositions into indecomposable summands. This answers a question posed by M.C.R. Butler in the 1960’s.