Splitting length of Abelian mixed groups of torsion-free rank 1

Splitting length of a mixed Abelian group $G$ is defined as the smallest positive integer $n$ such that $\bigotimes\limits^nG$ splits. The task of determining the splitting length of mixed Abelian groups was formulated by Irwin, Khabbaz, and Rayna. In this paper, a criterion for determining whether $\bigotimes\limits^nG$ splits for countable mixed Abelian groups $G$ of torsion-free rank 1 is found.