Retractable and coretractable abelian groups

In the theory of modules, an important role is played by the retractable and coretractable modules, which were introduced by Khuri (1979) and Amini, Ershad and Sharif (2009), respectively. In this paper, we study retractable and coretractable Abelian groups as modules over the ring of integers. In this case, the classical methods of the theory of Abelian groups are used, based on the injectivity and projectivity of divisible and free Abelian groups, respectively. This article provides complete descriptions of retractable and coretractable Abelian groups.