Geodesic
On a~class of modules over group rings of locally soluble groups
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 2, pp. 94-98

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A module $A$ over a group ring $DG$ is studied in the case when $D$ is a Dedekind domain, the group $G$ is locally soluble, the quotient module $A/C_A(G)$ is not an Artinian $D$-module, and the system of all subgroups $H\le G$ for which the quotient modules $A/C_A(H)$ are not Artinian $D$-modules satisfies the minimality condition for subgroups. Under these assumptions, it is proved that the group $G$ is hyperabelian and some properties of its periodic part are described.
Mots-clés : module
Keywords: group ring, locally soluble group. 
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     author = {O. Yu. Dashkova},
     title = {On a~class of modules over group rings of locally soluble groups},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {94--98},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2009_15_2_a8/}
}
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O. Yu. Dashkova. On a~class of modules over group rings of locally soluble groups. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 2, pp. 94-98. http://geodesic.mathdoc.fr/item/TIMM_2009_15_2_a8/