Dimension subgroups of metabelian p-groups
type: Item
instance of: scholarly article
title: Dimension subgroups of metabelian p-groups
zbMATH Open document ID: 0649.20004
DOI: 10.1016/0022-4049(88)90063-1
author: Narain Gupta
published in: Journal of Pure and Applied Algebra
publication date: 1988-01-01T00:00:00Z
review text: It is shown that if G is a metabelian p-group and \(D_ n(G)\) is the n-th dimension subgroup of G over the integers, then \(D_ n(G)\) coincides with the n-th term of the lower central series of G for \(n\leq 2p-1\). This is an improvement of previous work of the author on dimension subgroups of metabelian groups, and is proved by a finely balanced combination of techniques from the author's previous work with ideas of \textit{J. Sjogren} [ibid. 14, 175-194 (1979; Zbl 0395.20019)], as simplified by \textit{G. Cliff} and the reviewer [ibid. 47, 231-242 (1987; Zbl 0633.20004)]. The introduction contains a brief account of other work on dimension subgroups, particularly in the metabelian case.
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20F14
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 4059664
zbMATH Keywords: augmentation ideal
zbMATH Keywords: integral group ring
zbMATH Keywords: dimension subgroup
zbMATH Keywords: lower central series
zbMATH Keywords: metabelian groups
reviewed by: Brian Hartley
MaRDI profile type: Publication
full work available at URL: 0022-4049(88)90063-1
OpenAlex ID: W2041744566
cites work: Sjogren's theorem on dimension subgroups
cites work: On the dimension subgroups of metabelian groups
cites work: Q3767483
cites work: Q3658176
cites work: Dimension and lower central subgroups of metabelian p-groups
cites work: Q5617768
cites work: On the fourth integer dimension subgroup
cites work: Dimension and lower central subgroups
description: scientific article; zbMATH DE number 4059664