@article{Dashkova_2013, title={Locally soluble AFA-groups}, volume={65}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/2431}, abstractNote={Let $A$ be an $\mathbf{R}G$-module, where $\mathbf{R}$ is a ring, $G$ is a locally solvable group, $C_G (A) = 1$, and each proper subgroup $H$ of $G$ for which $A/C_A(H)$ is not an Artinian $\mathbf{R}$-module is finitely generated. It is proved that a locally solvable group $G$ that satisfies these conditions is hyperabelian if R is a Dedekind ring. We describe the structure of $G$ in the case where $G$ is a finitely generated solvable group, $A/C_A(H)$ is not an Artinian $\mathbf{R}$-module and $\mathbf{R}$ is a Dedekind ring.}, number={4}, journal={Ukrainsâ€™kyi Matematychnyi Zhurnal}, author={Dashkova, O. Yu.}, year={2013}, month={Apr.}, pages={459-469} }