Geodesic
On modules over group rings of locally soluble groups for a~ring of $p$-adic integers
Algebra and discrete mathematics, no. 1 (2009), pp. 32-43.

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The author studies the ${\bf Z_{p^{\infty}}}G$-module $A$ such that $\bf Z_{p^{\infty}}$ is a ring of $p$-adic integers, a group $G$ is locally soluble, the quotient module $A/C_{A}(G)$ is not Artinian $\bf Z_{p^{\infty}}$-module, and the system of all subgroups $H \leq G$ for which the quotient\linebreak modules $A/C_{A}(H)$ are not Artinian $\bf Z_{p^{\infty}}$-modules satisfies the minimal condition on subgroups. It is proved that the group $G$ under consideration is soluble and some its properties are obtained.
Keywords: Linear group, Artinian module, locally soluble group. 
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     author = {O. Yu. Dashkova},
     title = {On modules over group rings of locally soluble groups for a~ring of $p$-adic integers},
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     pages = {32--43},
     publisher = {mathdoc},
     number = {1},
     year = {2009},
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     url = {http://geodesic.mathdoc.fr/item/ADM_2009_1_a4/}
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O. Yu. Dashkova. On modules over group rings of locally soluble groups for a~ring of $p$-adic integers. Algebra and discrete mathematics, no. 1 (2009), pp. 32-43. http://geodesic.mathdoc.fr/item/ADM_2009_1_a4/