Scopes reduction and Morita equivalence classes of blocks in finite classical groups. II.
type: Item
instance of: scholarly article
title: Scopes reduction and Morita equivalence classes of blocks in finite classical groups. II.
zbMATH Open document ID: 1072.20012
author: Gerhard Hiss
author: Radha Kessar
published in: Journal of Algebra
publication date: 2005-02-22T00:00:00Z
review text: [For part I cf. the authors, ibid. 230, No. 2, 378-423 (2000; Zbl 0961.20036)]. Donovan has conjectured that, for any prime \(p\) and any finite \(p\)-group \(D\), the number of Morita equivalence classes of \(p\)-blocks of finite groups with defect group \(D\) is finite. In the paper under review, the authors are concerned with this conjecture for unipotent \(p\)-blocks of one of the classical groups \(\text{SL}_n(q)\), \(\text{SU}_n(q)\), \(\text{SO}_{2n+1}(q)\), \(\text{Sp}_{2n}(q)\) and \(\text{SO}^\pm_{2n}(q)\). For these groups and blocks, they obtain a reduction to the following situations: (1) \(\text{SU}_n(q)\), \(\text{SO}_{2n+1}(q)\), \(\text{Sp}_{2n}(q)\), \(\text{SO}^\pm_{2n}(q)\) for some \(n\) bounded in terms of \(|D|\); (2) \(\text{SO}^\pm_{2n}(q)\) for some \(n\) and some prime power \(q\equiv -1\pmod p\). Their proof is based on a new general criterion for Morita (and Puig) equivalences of blocks.
reviewed by: Burkhard Külshammer
Mathematics Subject Classification ID: 20C33
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G40
zbMATH DE Number: 2136595
zbMATH Keywords: numbers of blocks
zbMATH Keywords: defect groups
zbMATH Keywords: Morita equivalences
zbMATH Keywords: Puig equivalences
zbMATH Keywords: Donovan conjecture
zbMATH Keywords: classical groups
describes a project that uses: CHEVIE
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2004.08.030
OpenAlex ID: W2078223833
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DOI: 10.1016/J.JALGEBRA.2004.08.030
description: scientific article; zbMATH DE number 2136595