Note on a p-block of a finite group with Abelian defect group
type: Item
instance of: scholarly article
title: Note on a p-block of a finite group with Abelian defect group
zbMATH Open document ID: 0709.20011
author: Atumi Watanabe
published in: Osaka Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: Let G be a finite group and B a p-block of G with abelian defect group D. Let T(b) be the inertial group of a root b of B in \(C_ G(D)\). Let \(B_ 1\) be the block corresponding to b in \(C_ G(D_ 1)\), where \(D_ 1=C_ D(T(b))\). The author has earlier proved that there are strong numerical (and other) relations between the blocks B and \(B_ 1\). Here this study is continued to include information about lower defect group multiplicities and in particular the elementary divisors of the Cartan matrices. There is also a result about a vertex preserving bijection between a set of indecomposable modules in \(B_ 1\) and a set of indecomposable modules in B.
Mathematics Subject Classification ID: 20C20
zbMATH DE Number: 4165158
zbMATH Keywords: finite group
zbMATH Keywords: p-block
zbMATH Keywords: abelian defect group
zbMATH Keywords: inertial group
zbMATH Keywords: lower defect group
zbMATH Keywords: elementary divisors of the Cartan matrices
zbMATH Keywords: vertex
zbMATH Keywords: indecomposable modules
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4165158