$On modules over group rings of locally soluble groups for a ring of $p$-adic integers$

On modules over group rings of locally soluble groups for a ring of $p$-adic integers

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 whic...

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Бібліографічні деталі
Дата:	2018
Автор:	Dashkova, O. Yu.
Формат:	Стаття
Мова:	English
Опубліковано:	Lugansk National Taras Shevchenko University 2018
Теми:	Linear group Artinian module locally soluble group 20F19 20H25
Онлайн доступ:	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/767
Теги:	Додати тег Немає тегів, Будьте першим, хто поставить тег для цього запису!
Назва журналу:	Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics

id	admjournalluguniveduua-article-767
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spelling	admjournalluguniveduua-article-7672018-04-04T08:31:48Z On modules over group rings of locally soluble groups for a ring of $p$-adic integers Dashkova, O. Yu. Linear group, Artinian module, locally soluble group 20F19; 20H25 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 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. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/767 Algebra and Discrete Mathematics; Vol 8, No 1 (2009) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/767/297 Copyright (c) 2018 Algebra and Discrete Mathematics
institution	Algebra and Discrete Mathematics
baseUrl_str
datestamp_date	2018-04-04T08:31:48Z
collection	OJS
language	English
topic	Linear group Artinian module locally soluble group 20F19 20H25
spellingShingle	Linear group Artinian module locally soluble group 20F19 20H25 Dashkova, O. Yu. On modules over group rings of locally soluble groups for a ring of $p$-adic integers
topic_facet	Linear group Artinian module locally soluble group 20F19 20H25
format	Article
author	Dashkova, O. Yu.
author_facet	Dashkova, O. Yu.
author_sort	Dashkova, O. Yu.
title	On modules over group rings of locally soluble groups for a ring of $p$-adic integers
title_short	On modules over group rings of locally soluble groups for a ring of $p$-adic integers
title_full	On modules over group rings of locally soluble groups for a ring of $p$-adic integers
title_fullStr	On modules over group rings of locally soluble groups for a ring of $p$-adic integers
title_full_unstemmed	On modules over group rings of locally soluble groups for a ring of $p$-adic integers
title_sort	on modules over group rings of locally soluble groups for a ring of $p$-adic integers
description	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 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.
publisher	Lugansk National Taras Shevchenko University
publishDate	2018
url	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/767
work_keys_str_mv	AT dashkovaoyu onmodulesovergroupringsoflocallysolublegroupsforaringofpadicintegers
first_indexed	2025-12-02T15:40:57Z
last_indexed	2025-12-02T15:40:57Z
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On modules over group rings of locally soluble groups for a ring of \(p\)-adic integers

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