The nilpotency class of the unit group of a modular group algebra. III
type: Item
instance of: scholarly article
title: The nilpotency class of the unit group of a modular group algebra. III
zbMATH Open document ID: 0818.16025
DOI: 10.1007/BF01199099
published in: Archiv der Mathematik
publication date: 1995-08-14T00:00:00Z
review text: The author continues the study of the nilpotency class of the unit group of a modular group algebra [Part I, Isr. J. Math. 70, 257-266 (1990; Zbl 0713.16020); Part II, ibid., 267-277 (1990; Zbl 0693.16008)]. A recent result of \textit{X. Du} [Can. Math. Bull. 35, 174-179 (1992; Zbl 0801.16019)] combined with that of \textit{A. K. Bhandari} and the reviewer [Bull. Lond. Math. Soc. 24, 68-70 (1992; Zbl 0777.20004)] shows that the nilpotency class of the unit group is determined by the orders of the Lie dimension subgroups, provided the characteristic \(\geq 5\). Exploiting the techniques developed earlier by the author for the study of Lie dimension subgroups [J. Lond. Math. Soc., II. Ser. 43, 23-46 (1991; Zbl 0669.16015)], some very interesting further results are obtained for the nilpotency class of the unit groups of group algebras under the above restriction on the characteristic.
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20F14
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 572581
zbMATH Keywords: nilpotency classes
zbMATH Keywords: modular group algebras
zbMATH Keywords: Lie dimension subgroups
zbMATH Keywords: unit groups
author: Aner Shalev
reviewed by: Inder Bir S. Passi
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01199099
OpenAlex ID: W4256700548
description: scientific article; zbMATH DE number 572581