Geodesic
On one class of modules that are close to Noetherian
Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 7, pp. 113-125 
O. Yu. Dashkova. On one class of modules that are close to Noetherian. Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 7, pp. 113-125. http://geodesic.mathdoc.fr/item/FPM_2009_15_7_a3/
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     author = {O. Yu. Dashkova},
     title = {On one class of modules that are close to {Noetherian}},
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     volume = {15},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2009_15_7_a3/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider an $\mathbf RG$-module $A$ over a commutative Noetherian ring $\mathbf R$. Let $G$ be a group having infinite section $p$-rank (or infinite 0-rank) such that $C_G(A)=1$, $A/C_A(G)$ is not a Noetherian $\mathbf R$-module, but the quotient $A/C_A(H)$ is a Noetherian $\mathbf R$-module for every proper subgroup $H$ of infinite section $p$-rank (or infinite 0-rank, respectively). In this paper, it is proved that if $G$ is a locally soluble group, then $G$ is soluble. Some properties of soluble groups of this type are also obtained.

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