Geodesic
On locally soluble $AFN$-groups
Algebra and discrete mathematics, Tome 14 (2012) no. 1, pp. 37-48

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Let $A$ be an $\mathbf{R}G$-module, where $\bf R$ is a commutative ring, $G$ is a locally soluble group, $C_{G}(A)=1$, and each proper subgroup $H$ of $G$ for which $A/C_{A}(H)$ is not a noetherian $\bf R$-module, is finitely generated. We describe the structure of a locally soluble group $G$ with these conditions and the structure of $G$ under consideration if $G$ is a finitely generated soluble group and the quotient module $A/C_{A}(G)$ is not a noetherian $\bf R$-module.
Keywords: locally soluble group, noetherian module, group ring. 
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     author = {Olga Yu. Dashkova},
     title = {On locally soluble $AFN$-groups},
     journal = {Algebra and discrete mathematics},
     pages = {37--48},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2012_14_1_a4/}
}
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Olga Yu. Dashkova. On locally soluble $AFN$-groups. Algebra and discrete mathematics, Tome 14 (2012) no. 1, pp. 37-48. http://geodesic.mathdoc.fr/item/ADM_2012_14_1_a4/