Idempotente im Burnsidering modulo Primzahlpotenzen: Bemerkungen zu einer Arbeit von E. Jacobson. (Idempotents in the Burnside ring modulo prime powers: Remarks on a work by E. Jacobson)
type: Item
instance of: scholarly article
title: Idempotente im Burnsidering modulo Primzahlpotenzen: Bemerkungen zu einer Arbeit von E. Jacobson. (Idempotents in the Burnside ring modulo prime powers: Remarks on a work by E. Jacobson)
zbMATH Open document ID: 0656.20002
DOI: 10.1007/BF01207474
published in: Archiv der Mathematik
publication date: 1988-01-01T00:00:00Z
review text: Let G be a finite group, and denote by B(G) the Burnside ring of G. That is, B(G) is the Grothendieck ring of finite sets with G-action. The author determines the primitive idempotents in the localization of B(G) at a prime p, in the completion thereof, and in the reduction modulo \(p^ n\), for any \(n\geq 1\). This makes explicit an enumeration of the idempotents given by \textit{E. Jacobson} [J. Algebra 99, 58-71 (1986; Zbl 0585.20002)].
Mathematics Subject Classification ID: 20B99
Mathematics Subject Classification ID: 18F30
Mathematics Subject Classification ID: 16U99
Mathematics Subject Classification ID: 20C99
zbMATH DE Number: 4071166
zbMATH Keywords: finite group
zbMATH Keywords: Burnside ring
zbMATH Keywords: Grothendieck ring
zbMATH Keywords: primitive idempotents
author: Helmut Krämer
reviewed by: William H. Gustafson
MaRDI profile type: Publication
cites work: A characterisation of solvable groups
cites work: Idempotent formula for the Burnside algebra with applications to the \(p\)-subgroup simplicial complex.
cites work: The Burnside ring modulo a prime
cites work: Q3869440
cites work: The Burnside algebra of a finite group
full work available at URL: https://doi.org/10.1007/bf01207474
OpenAlex ID: W80766616
description: scientific article; zbMATH DE number 4071166