Locally soluble AFA-groups - Dashkova, O. Yu. (Ukrains’kyi Matematychnyi Zhurnal, 2013)
Let A be an RG-module, where 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 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 R-module and R is a Dedekind ring.