Perfect isometries for principal blocks with Abelian defect groups and elementary Abelian \(2\)-inertial quotients
type: Item
instance of: scholarly article
title: Perfect isometries for principal blocks with Abelian defect groups and elementary Abelian \(2\)-inertial quotients
zbMATH Open document ID: 0888.20007
author: Yoko Usami
published in: Journal of Algebra
publication date: 1997-12-14T00:00:00Z
review text: Let \(p\geq 5\) be a prime number, let \(G\) be a finite group with abelian Sylow \(p\)-subgroup \(P\), and suppose that \(N_G(P)/C_G(P)\) is either an elementary abelian 2-group or dihedral of order 8. The authors shows that the principal \(p\)-blocks of \(G\) and \(N_G(P)\) are isotypic.
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C05
zbMATH DE Number: 1088603
zbMATH Keywords: isotypies
zbMATH Keywords: perfect isometries
zbMATH Keywords: Dade conjecture
zbMATH Keywords: Broué conjecture
zbMATH Keywords: Abelian Sylow subgroups
zbMATH Keywords: principal \(p\)-blocks
zbMATH Keywords: finite groups
reviewed by: Burkhard Külshammer
MaRDI profile type: Publication
full work available at URL: jabr.1997.7094
OpenAlex ID: W2057663827
cites work: Q3804896
cites work: Local methods in block theory
cites work: Q4279639
cites work: A Frobenius theorem for blocks
cites work: Q5639853
cites work: Some applications of the theory of blocks of characters of finite groups. IV
cites work: Q3483449
cites work: Counting characters in blocks. I
cites work: On perfect isometries and isotypies in finite groups
cites work: Q5577154
cites work: Crossed products and blocks with normal defect groups
cites work: Pointed groups and construction of characters
cites work: Pointed groups and construction of modules
cites work: Perfect isometries for blocks with abelian defect groups and Klein four inertial quotients
cites work: Perfect isometries for blocks with abelian defect groups and cyclic inertial quotients of order \(4\)
cites work: Perfect isometries in the blocks with abelian defect of symmetric and sporadic groups
cites work: Perfect isometries and isotypies for blocks with abelian defect groups and the inertial quotients isomorphic to \(\mathbb{Z}_ 4\times\mathbb{Z}_ 2\)
cites work: Perfect isometries and isotypies for blocks with Abelian defect groups and the inertial quotients isomorphic to \(\mathbf Z_ 3\times\mathbf Z_ 3\)
DOI: 10.1006/JABR.1997.7094
description: scientific article; zbMATH DE number 1088603