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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 Zp∞G-module A such that Zp∞ is a ring of p-adic integers, a group G is locally soluble, the quotient module A/CA(G) is not Artinian Zp∞-module, and the system of all subgroups H≤G for which the quotient modules A/CA(H) are not Artinian Zp∞-modules satisfies the minimal conditi...

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Main Author: Dashkova, O.Yu.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2009
Series:Algebra and Discrete Mathematics
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/154573
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spelling irk-123456789-1545732019-06-16T01:25:29Z On modules over group rings of locally soluble groups for a ring of p -adic integers Dashkova, O.Yu. The author studies the Zp∞G-module A such that Zp∞ is a ring of p-adic integers, a group G is locally soluble, the quotient module A/CA(G) is not Artinian Zp∞-module, and the system of all subgroups H≤G for which the quotient modules A/CA(H) are not Artinian Zp∞-modules satisfies the minimal condition on subgroups. It is proved that the group G under consideration is soluble and some its properties are obtained. 2009 Article On modules over group rings of locally soluble groups for a ring of p -adic integers / O. Yu. Dashkova // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 1. — С. 32–43. — Бібліогр.: 9 назв. — англ. 1726-3255 2000 Mathematics Subject Classification: 20F19; 20H25. http://dspace.nbuv.gov.ua/handle/123456789/154573 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description The author studies the Zp∞G-module A such that Zp∞ is a ring of p-adic integers, a group G is locally soluble, the quotient module A/CA(G) is not Artinian Zp∞-module, and the system of all subgroups H≤G for which the quotient modules A/CA(H) are not Artinian Zp∞-modules satisfies the minimal condition on subgroups. It is proved that the group G under consideration is soluble and some its properties are obtained.
format Article
author Dashkova, O.Yu.
spellingShingle Dashkova, O.Yu.
On modules over group rings of locally soluble groups for a ring of p -adic integers
Algebra and Discrete Mathematics
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
publisher Інститут прикладної математики і механіки НАН України
publishDate 2009
url http://dspace.nbuv.gov.ua/handle/123456789/154573
citation_txt On modules over group rings of locally soluble groups for a ring of p -adic integers / O. Yu. Dashkova // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 1. — С. 32–43. — Бібліогр.: 9 назв. — англ.
series Algebra and Discrete Mathematics
work_keys_str_mv AT dashkovaoyu onmodulesovergroupringsoflocallysolublegroupsforaringofpadicintegers
first_indexed 2023-05-20T17:38:50Z
last_indexed 2023-05-20T17:38:50Z
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