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 PFMT, 2011, Issue 4(9), Pages 100–105 (Mi pfmt139)

MATHEMATICS

On modules over group rings of locally finite groups

O. Yu. Dashkova

O. Honchar Dnepropetrovsk National University, Dnepropetrovsk, Ukraine

Abstract: Let $A$ be an $\mathrm{R}G$-module, where $\mathbf{R}$ is a commutative ring with the unit, $A/C_A(G)$ is not an artinian $\mathbf{R}$-module, $C_G(A) = 1$ and $G$ is a locally finite group. Let $\mathfrak{L}_{nad}(G)$ be a system of all subgroups $H \le G$ such that quotient modules $A/C_A(H)$ are not artinian $\mathbf{R}$-modules. The author studies $\mathbf{R}G$-module $A$ such that $\mathfrak{L}_{nad}(G)$ satisfies either weak minimal condition or weak maximal condition as an ordered set. The properties of the locally finite group $G$ with these conditions are described. Some properties of a locally soluble periodic group $G$ under consideration are obtained if $\mathbf{R}$ is a dedekind ring.

Keywords: an artinian $\mathbf{R}$-module, a group ring, a locally finite group

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UDC: 512.544

Citation: O. Yu. Dashkova, “On modules over group rings of locally finite groups”, PFMT, 2011, no. 4(9), 100–105

Citation in format AMSBIB
\Bibitem{Das11} \by O.~Yu.~Dashkova \paper On modules over group rings of locally finite groups \jour PFMT \yr 2011 \issue 4(9) \pages 100--105 \mathnet{http://mi.mathnet.ru/pfmt139}