The 5-modular characters of the McLaughlin group and its covering group
type: Item
instance of: scholarly article
title: The 5-modular characters of the McLaughlin group and its covering group
zbMATH Open document ID: 0753.20003
DOI: 10.1007/BF02567631
author: Gerhard Hiss
author: Klaus Lux
author: Richard A. Parker
published in: Manuscripta Mathematica
publication date: 1992-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/155657
review text: The authors determine the irreducible Brauer characters and the corresponding decomposition matrices in characteristic 5 for the 3-fold cover \(\hat 3 McL\) of McLaughlin's sporadic simple group \(McL\) of order \(2^ 7\cdot 3^ 6\cdot 5^ 3 \cdot 7\cdot 11\). Apart from 5-blocks of defect 0 the group \(\hat 3 McL\) has three further 5-blocks, the principal block \(B_ 0\) and one ``dual'' pair, say \(B_ 1\), and \(B_ 2=B_ 1^*\) all of which have maximal defect. According to the authors' rule of thumb they use at least one new trick for each block under consideration in order to achieve their goal. On top of that they use the computer system MOC and methods that have become quite standard in that area of research these days, e.g. condensation methods of the Meat-Axe, induction-restriction methods, Nakayama relations, structure of indecomposable modules in a block with cyclic defect group (of order 5 in the present case). It may be worth noting that prior to this work, \textit{A. J. Woldar} [Commun. Algebra 14, 277-291 (1986; Zbl 0581.20007)] determined all but two irreducible Brauer characters of the principal block \(B_ 0\).
Mathematics Subject Classification ID: 20C34
Mathematics Subject Classification ID: 20C20
zbMATH DE Number: 60117
zbMATH Keywords: irreducible Brauer characters
zbMATH Keywords: decomposition matrices
zbMATH Keywords: McLaughlin's sporadic simple group
zbMATH Keywords: principal block
zbMATH Keywords: maximal defect
zbMATH Keywords: Meat-Axe
zbMATH Keywords: indecomposable modules
reviewed by: Wolfgang Lempken
describes a project that uses: CAS
MaRDI profile type: Publication
cites work: Nilpotent elements in the Green ring
cites work: Q3684278
cites work: Q3955560
cites work: Q3993433
cites work: Q3035669
cites work: Q4012094
cites work: Computer condensation of modular representations
cites work: On the 5-decomposition matrix for mclaughlin's sporadic simple group
OpenAlex ID: W2025441136
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description: scientific article; zbMATH DE number 60117