The structure of the projective indecomposable modules of the Mathieu group \(M_{12}\) in characteristic 2 and 3
type: Item
instance of: scholarly article
title: The structure of the projective indecomposable modules of the Mathieu group \(M_{12}\) in characteristic 2 and 3
zbMATH Open document ID: 0784.20003
DOI: 10.1007/BF01207185
author: Gerhard J. A. Schneider
published in: Archiv der Mathematik
publication date: 1993-11-15T00:00:00Z
review text: In this note the author determines the socle structure of the projective indecomposable modules for the Mathieu group \(M_{12}\) in characteristic 2 and 3. So as byproduct \(\text{Ext}^ 1\) for simple modules can be read off directly. The proofs are based on computer computations using mainly CAYLEY and MEATAXE. For the determination of the socle structure algorithms are used which have been developed by the author himself [J. Symb. Comput. 9, 607- 636 (1990; Zbl 0703.20009); Computing with homomorphisms of modular representations (preprint)]. In the meantime these are also part of CAYLEY.
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C34
Mathematics Subject Classification ID: 20C40
zbMATH DE Number: 446304
zbMATH Keywords: projective indecomposable modules
zbMATH Keywords: Mathieu group \(M_{12}\)
zbMATH Keywords: simple modules
zbMATH Keywords: CAYLEY
zbMATH Keywords: MEATAXE
reviewed by: Wolfgang Willems
MaRDI profile type: Publication
cites work: Q3333220
cites work: Q3684278
cites work: Operation of class sums on permutation modules
cites work: The modular characters of the Mathieu groups
cites work: Q3035669
cites work: Computing with endomorphism rings of modular representations
cites work: The Structure of the Projective Indecomposable Modules of the Suzuki Group Sz(8) in Characteristic 2
description: scientific article; zbMATH DE number 446304