Geodesic
Modules over group rings of solvable groups with rank restrictions on subgroups
Matematičeskie trudy, Tome 15 (2012) no. 1, pp. 74-85.

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Let $A$ be an $\mathbf RG$-module over a commutative ring $\mathbf R$, where $G$ is a group of infinite section $p$-rank ($0$-rank), $C_G(A)=1$, $A$ is not a Noetherian $\mathbf R$-module, and the quotient $A/C_A(H)$ is a Noetherian $\mathbf R$-module for every proper subgroup $H$ of infinite section $p$-rank ($0$-rank). We describe the structure of solvable groups $G$ of this type. 
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O. Yu. Dashkova. Modules over group rings of solvable groups with rank restrictions on subgroups. Matematičeskie trudy, Tome 15 (2012) no. 1, pp. 74-85. http://geodesic.mathdoc.fr/item/MT_2012_15_1_a3/

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