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Algebra Discrete Math., 2012, Volume 14, Issue 1, Pages 37–48 (Mi adm83)  

This article is cited in 1 scientific paper (total in 1 paper)

RESEARCH ARTICLE

On locally soluble $AFN$-groups

Olga Yu. Dashkova

49055, Ukraine, Dnepropetrovsk, prospekt Kirova, 102-D, kv. 35

Abstract: Let $A$ be an $\mathbf{R}G$-module, where $\bf R$ is a commutative ring, $G$ is a locally soluble group, $C_{G}(A)=1$, and each proper subgroup $H$ of $G$ for which $A/C_{A}(H)$ is not a noetherian $\bf R$-module, is finitely generated. We describe the structure of a locally soluble group $G$ with these conditions and the structure of $G$ under consideration if $G$ is a finitely generated soluble group and the quotient module $A/C_{A}(G)$ is not a noetherian $\bf R$-module.

Keywords: locally soluble group, noetherian module, group ring.

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Bibliographic databases:
MSC: 20F19
Received: 21.04.2012
Revised: 02.10.2012
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Citation: Olga Yu. Dashkova, “On locally soluble $AFN$-groups”, Algebra Discrete Math., 14:1 (2012), 37–48

Citation in format AMSBIB
\Bibitem{Das12}
\by Olga~Yu.~Dashkova
\paper On locally soluble $AFN$-groups
\jour Algebra Discrete Math.
\yr 2012
\vol 14
\issue 1
\pages 37--48
\mathnet{http://mi.mathnet.ru/adm83}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3052320}
\zmath{https://zbmath.org/?q=an:06110035}


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    This publication is cited in the following articles:
    1. O. Yu. Dashkova, “Obobschenno razreshimye $\mathrm{AFM}$-gruppy”, Tr. In-ta matem., 21:1 (2013), 52–62  mathnet
  • Algebra and Discrete Mathematics
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