Modular representations of Loewy length two.
type: Item
instance of: scholarly article
title: Modular representations of Loewy length two.
zbMATH Open document ID: 1066.20009
DOI: 10.1155/S0161171203210681
author: S. Bouhamidi
author: Mohamed E. Charkani
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-09T00:00:00Z
full work available at URL: https://eudml.org/doc/51440
review text: Summary: Let \(G\) be a finite \(p\)-group, \(K\) a field of characteristic \(p\), and \(J\) the radical of the group algebra \(K[G]\). We study modular representations using some new results of the theory of extensions of modules. More precisely, we describe the \(K[G]\)-modules \(M\) such that \(J^2M=0\) and give some properties and isomorphism invariants which allow us to compute the number of isomorphism classes of \(K[G]\)-modules \(M\) such that \(\dim_K(M)=\mu(M)+1\), where \(\mu(M)\) is the minimum number of generators of the \(K[G]\)-module \(M\). We also compute the number of isomorphism classes of indecomposable \(K[G]\)-modules \(M\) such that \(\dim_K(\text{Rad}(M))=1\).
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C05
zbMATH DE Number: 2166341
zbMATH Keywords: finite \(p\)-groups
zbMATH Keywords: group algebras
zbMATH Keywords: modular representations
zbMATH Keywords: extensions of modules
zbMATH Keywords: numbers of isomorphism classes
zbMATH Keywords: indecomposable modules
MaRDI profile type: Publication
OpenAlex ID: W2140751415
description: scientific article; zbMATH DE number 2166341