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Algebra and Discrete Mathematics, 2009, Issue 1, Pages 32–43
(Mi adm106)
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This article is cited in 1 scientific paper (total in 1 paper)
RESEARCH ARTICLE
On modules over group rings of locally soluble groups for a ring of $p$-adic integers
O. Yu. Dashkova Department of Mathematics and Mechanics, Kyev National University, ul. ladimirskaya, 60, Kyev, 01033, Ukraine
Abstract:
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.
Received: 22.03.2009 Revised: 30.04.2009
Citation:
O. Yu. Dashkova, “On modules over group rings of locally soluble groups for a ring of $p$-adic integers”, Algebra Discrete Math., 2009, no. 1, 32–43
Linking options:
https://www.mathnet.ru/eng/adm106 https://www.mathnet.ru/eng/adm/y2009/i1/p32
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Abstract page: | 119 | Full-text PDF : | 55 | First page: | 1 |
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