The nilpotency class of the unit group of a modular group algebra. II
type: Item
instance of: scholarly article
title: The nilpotency class of the unit group of a modular group algebra. II
zbMATH Open document ID: 0693.16008
DOI: 10.1007/BF02801464
author: Avinoam Mann
author: Aner Shalev
published in: Israel Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: For a finite p-group G, let U(G) be the unit group of the group algebra of G over a field of p elements. It is known that if \(| G'| =p\), the nilpotency class of U(G) is p. The main result of the present paper states, that if \(| G'| >p\), the same nilpotency class is at least 2p-1. Equality holds if G has class 2 and \(| G'| =p^ 2\) [part I, by \textit{A. Shalev} alone, is also going to appear in the same Journal].
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20D15
zbMATH DE Number: 4134248
zbMATH Keywords: finite p-group
zbMATH Keywords: unit group
zbMATH Keywords: group algebra
zbMATH Keywords: nilpotency class
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02801464
OpenAlex ID: W2154270531
description: scientific article; zbMATH DE number 4134248