Augmentation powers and group homology.
type: Item
instance of: scholarly article
title: Augmentation powers and group homology.
zbMATH Open document ID: 1059.16017
author: Roman Mikhailov
author: Inder Bir S. Passi
published in: Journal of Pure and Applied Algebra
publication date: 2004-08-19T00:00:00Z
review text: It is well-known that low-dimensional group homology provides a useful tool for studying lower central series, dimension subgroups and augmentation powers of group rings. The aim of this paper is to extend these methods to the study of transfinite augmentation powers and, more generally, to the study of two-sided ideals in group rings and the normal subgroups determined by them. The authors generalize the notion of polynomial 2-cocycles and use a homological approach to the identification of normal subgroups, determined by two-sided ideals of the group rings \(RG\), where \(R\) is the ring of integers or the field of rational numbers. In particular, they investigate transfinite dimension subgroups, determined by the transfinite powers of the augmentation ideals in \(RG\).
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20C07
Mathematics Subject Classification ID: 20F14
Mathematics Subject Classification ID: 16D25
Mathematics Subject Classification ID: 20J05
zbMATH DE Number: 2093430
zbMATH Keywords: group rings
zbMATH Keywords: augmentation powers
zbMATH Keywords: dimension subgroups
zbMATH Keywords: group homology
reviewed by: S. V. Mihovski
MaRDI profile type: Publication
full work available at URL: j.jpaa.2004.01.005
OpenAlex ID: W2166089734
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DOI: 10.1016/J.JPAA.2004.01.005
description: scientific article; zbMATH DE number 2093430