The symmetry of the modular Burnside ring
type: Item
instance of: scholarly article
title: The symmetry of the modular Burnside ring
zbMATH Open document ID: 0962.20005
author: Markus Deiml
published in: Journal of Algebra
publication date: 2001-03-18T00:00:00Z
review text: Let \(k\) be a field of characteristic \(p>0\), \(G\) be a finite group, \(b(G)\) be the Burnside ring of \(G\) and let \(B_k(G)=k\otimes_\mathbb{Z} b(G)\). The blocks of \(B_k(G)\) are parametrized by the conjugacy classes of subgroups \(H\) of \(G\) satisfying \(O^p(H)=H\). The author proves that the block \(B_H\) of \(B_k(G)\) is a symmetric \(k\)-algebra if and only if \(|N_G(H):H|\) is not divisible by \(p^2\).
reviewed by: Andrei Marcus
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 19A22
zbMATH DE Number: 1471818
zbMATH Keywords: finite groups
zbMATH Keywords: Burnside rings
zbMATH Keywords: symmetric algebras
MaRDI profile type: Publication
full work available at URL: jabr.1999.8218
OpenAlex ID: W2091266190
cites work: Q4724810
cites work: A characterisation of solvable groups
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cites work: The Burnside algebra of a finite group
cites work: Idempotents of Burnside rings and Dress induction theorem
cites work: On the unit groups of Burnside rings
DOI: 10.1006/JABR.1999.8218
description: scientific article; zbMATH DE number 1471818