On defect groups of the Mackey algebras for finite groups
type: Item
instance of: scholarly article
title: On defect groups of the Mackey algebras for finite groups
zbMATH Open document ID: 0884.20005
author: Fumihito Oda
published in: Hokkaido Mathematical Journal
publication date: 1998-03-31T00:00:00Z
review text: Let \(G\) be a finite group and \(R\) a commutative ring. The Mackey algebra \(\mu_R(G)\) was used by J. Thévenaz and P. Webb in connection with their work on Mackey functors. It appeared in earlier work by T. Yoshida under the name ``span ring''. When \(R\) is a field of characteristic \(p\) then the blocks of \(\mu_R(G)\) can be parametrized by conjugacy classes of pairs \((J,B)\) consisting of a \(p\)-perfect subgroup \(J\) of \(G\) and a block \(B\) of the group algebra \(R[N_G(J)/J]\). The author defines the defect groups of a block of \(\mu_R(G)\) in terms of a certain Green functor. For a block \(B\) of \(RG\), the defect groups of \(B\) are shown to be contained in defect groups of the block of \(\mu_R(G)\) parametrized by \((1,B)\).
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20C20
zbMATH DE Number: 1054034
zbMATH Keywords: finite groups
zbMATH Keywords: Mackey algebras
zbMATH Keywords: Mackey functors
zbMATH Keywords: blocks
zbMATH Keywords: \(p\)-perfect subgroups
zbMATH Keywords: group algebras
zbMATH Keywords: defect groups
reviewed by: Burkhard Külshammer
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1351257972
OpenAlex ID: W2092623713
DOI: 10.14492/HOKMJ/1351257972
description: scientific article; zbMATH DE number 1054034