On circle groups of nilpotent rings of characteristic \(2\)
type: Item
instance of: scholarly article
title: On circle groups of nilpotent rings of characteristic \(2\)
zbMATH Open document ID: 0858.16028
DOI: 10.1007/BF01879729
published in: Periodica Mathematica Hungarica
publication date: 1997-03-06T00:00:00Z
review text: The author proves that a nilpotent group of class 2 and exponent 4 is a circle group of a nilpotent ring of index 3 and characteristic 2. For any radical ring \(R\) one denotes the group \(R\) with multiplication \(\circ\) obtained by \(a\circ b:=a+b+ab\) for any two \(a,b\in R\) the circle group of \(R\). The question on the appearance of a nilpotent group as a circle group has applications to questions concerning the unit group of a group ring.
reviewed by: Alexander Zimmermann
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 16N40
Mathematics Subject Classification ID: 20F18
Mathematics Subject Classification ID: 20C05
zbMATH DE Number: 926938
zbMATH Keywords: nilpotent groups of class 2 and exponent 4
zbMATH Keywords: circle groups
zbMATH Keywords: nilpotent rings
zbMATH Keywords: radical rings
zbMATH Keywords: unit groups
zbMATH Keywords: group rings
author: Adalbert Bovdi
MaRDI profile type: Publication
cites work: Circle Groups of Nilpotent Rings
cites work: Structure of group bases of a group ring
cites work: Q3724495
cites work: The second augmentation quotient of an integral group ring
cites work: On the Circle Group of a Nilpotent Ring
cites work: The modular group algebra of a central-elementary-by-abelian p-group
description: scientific article; zbMATH DE number 926938