TY - JOUR
AU - O. Yu. Dashkova
PY - 2013/04/25
Y2 - 2023/03/27
TI - Locally soluble AFA-groups
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 65
IS - 4
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2431
AB - 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.
ER -