Splitting conjecture for two-dimensional torsion-free definable abelian groups

Let $\mathcal{M}$ be an o-minimal structure, and let $G$ be an abelian, two-dimensional, torsion-free group definable in $\mathcal{M}$. Splitting conjecture. The group $G$ is the product of two definable one-dimensional subgroups. This is the two-dimensional case of the definable splitting problem for linearizable abelian torsion-free definable groups. The supplied text does not state whether this claim has been resolved.