On a class of modules that are close to Noetherian.
type: Item
instance of: scholarly article
title: On a class of modules that are close to Noetherian.
zbMATH Open document ID: 1238.20051
published in: Journal of Mathematical Sciences (New York)
publication date: 2011-06-30T00:00:00Z
review text: Let \(RG\) be the group ring of a group \(G\) over a commutative Noetherian ring \(R\) and let \(A\) be an \(RG\)-module. In this paper the author finds sufficient conditions for \(A\) and \(G\) such that a locally soluble group \(G\) is soluble. For example, let \(G\) be a locally soluble group either of infinite Abelian section rank, or of infinite special rank. If the quotient \(R\)-module \(A/C_A(H)\) is Noetherian for every proper subgroup \(H\) of \(G\) such that \(H\) is, respectively, of infinite Abelian section rank or of infinite special rank, then \(G\) is soluble. Moreover, suppose that \(G\) is a locally soluble group with infinite \(p\)-rank \(r_p(G)\) for some prime number \(p\). If \(A/C_A(H)\) is Noetherian for every proper subgroup \(H\) with infinite \(p\)-rank \(r_p(H)\), then \(G\) is soluble.
Mathematics Subject Classification ID: 20F16
Mathematics Subject Classification ID: 20C07
Mathematics Subject Classification ID: 16P40
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20F19
zbMATH DE Number: 5915294
zbMATH Keywords: soluble groups
zbMATH Keywords: locally soluble groups
zbMATH Keywords: Abelian section rank
zbMATH Keywords: special rank
zbMATH Keywords: Noetherian modules
zbMATH Keywords: group rings
author: O. Yu. Dashkova
reviewed by: S. V. Mihovski
MaRDI profile type: Publication
full work available at URL: s10958-010-0064-1
OpenAlex ID: W2148090482
cites work: Radical groups of finite Abelian subgroup rank
cites work: Linear groups with rank restrictions on the subgroups of infinite central dimension.
cites work: The Schur property and groups with uniform conjugacy classes
cites work: Q5675882
cites work: Q5654235
cites work: Q5676405
DOI: 10.1007/S10958-010-0064-1
description: scientific article; zbMATH DE number 5915294