Locally soluble AFA-groups

  • O. Yu. Dashkova Днепропетр. нац. ун-т

Abstract

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.
Published
25.04.2013
How to Cite
DashkovaO. Y. “Locally Soluble AFA-Groups”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, no. 4, Apr. 2013, pp. 459-6, http://umj.imath.kiev.ua/index.php/umj/article/view/2431.
Section
Research articles