Broué's conjecture for non-principal 3-blocks of finite groups
type: Item
instance of: scholarly article
title: Broué's conjecture for non-principal 3-blocks of finite groups
zbMATH Open document ID: 1013.20009
DOI: 10.1016/S0022-4049(01)00170-0
author: Shigeo Koshitani
author: Naoko Kunugi
author: Katsushi Waki
published in: Journal of Pure and Applied Algebra
publication date: 2002-08-22T00:00:00Z
review text: Let \(G\) be the O'Nan finite simple group of order \(2^9\cdot 3^4\cdot 5\cdot 7^3\cdot 11\cdot 19\cdot 31\), and let \(A\) be the (non-principal) 3-block of \(G\) with elementary Abelian defect group \(D\) of order 9. The authors show that \(A\) is splendidly equivalent to its Brauer correspondent in \(N_G(D)\) and Puig equivalent to the principal 3-block of \(\text{PSL}(3,4)\). This verifies Broué's Abelian defect group conjecture for this block of \(G\). The authors also deal with the non-principal 3-block of maximal defect in the Higman-Sims finite simple group of order \(2^9\cdot 3^2\cdot 5^3\cdot 7 \cdot 11\) in a similar way.
reviewed by: Burkhard Külshammer
Mathematics Subject Classification ID: 20C34
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C05
zbMATH DE Number: 1787490
zbMATH Keywords: blocks
zbMATH Keywords: defect groups
zbMATH Keywords: Broué's conjecture
zbMATH Keywords: derived equivalences
zbMATH Keywords: splendid equivalences
zbMATH Keywords: trivial source modules
zbMATH Keywords: O'Nan simple group
zbMATH Keywords: Higman-Sims simple group
Wikidata QID: Q123241667
MaRDI profile type: Publication
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full work available at URL: s0022-4049(01)00170-0
OpenAlex ID: W1995616706
description: scientific article; zbMATH DE number 1787490