Geodesic
Locally soluble $\operatorname{AFN}$-groups
Problemy fiziki, matematiki i tehniki, no. 3 (2012), pp. 58-64

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Let $A$ be an $\textrm{R}G$-module, where $\textrm{R}$ is a commutative noetherian ring with the unit, $G$ is a locally soluble group, $C_G(A) = 1$, and each proper subgroup $H$ of a group $G$ for which $A/C_A(H)$ is not a noetherian $\textrm{R}$-module, is finitely generated. It is proved that a locally soluble group $G$ with these conditions is hyperabelian. It is described the structure of a group $G$ under consideration if $G$ is a finitely generated soluble group and the quotient module $A/C_A(G)$ is not a noetherian $\textrm{R}$-module.
Keywords: group ring, locally soluble group, noetherian $\textrm{R}$-module. 
@article{PFMT_2012_3_a10,
     author = {O. Yu. Dashkova},
     title = {Locally soluble $\operatorname{AFN}$-groups},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {58--64},
     publisher = {mathdoc},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2012_3_a10/}
}
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O. Yu. Dashkova. Locally soluble $\operatorname{AFN}$-groups. Problemy fiziki, matematiki i tehniki, no. 3 (2012), pp. 58-64. http://geodesic.mathdoc.fr/item/PFMT_2012_3_a10/