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Trudy Inst. Mat. i Mekh. UrO RAN, 2009, Volume 15, Number 2, Pages 94–98 (Mi timm226)  

This article is cited in 2 scientific papers (total in 2 papers)

On a class of modules over group rings of locally soluble groups

O. Yu. Dashkova

National Taras Shevchenko University of Kyiv, The Faculty of Mechanics and Mathematics

Abstract: 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.

Keywords: module, group ring, locally soluble group

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2009, 267, suppl. 1, S57–S61

Bibliographic databases:

UDC: 512.544
Received: 09.10.2008

Citation: O. Yu. Dashkova, “On a class of modules over group rings of locally soluble groups”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 2, 2009, 94–98; Proc. Steklov Inst. Math. (Suppl.), 267, suppl. 1 (2009), S57–S61

Citation in format AMSBIB
\Bibitem{Das09}
\by O.~Yu.~Dashkova
\paper On a~class of modules over group rings of locally soluble groups
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2009
\vol 15
\issue 2
\pages 94--98
\mathnet{http://mi.mathnet.ru/timm226}
\elib{http://elibrary.ru/item.asp?id=12878772}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2009
\vol 267
\issue , suppl. 1
\pages S57--S61
\crossref{https://doi.org/10.1134/S0081543809070062}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000274041900006}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. O. Yu. Dashkova, “O modulyakh nad gruppovymi koltsami lokalno konechnykh grupp”, PFMT, 2011, no. 4(9), 100–105  mathnet
    2. O. Yu. Dashkova, “Modules over integer group rings of locally soluble groups with minimax restriction”, J. Math. Sci., 187:2 (2012), 129–137  mathnet  crossref
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