International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 70, Pages 4399-4408
doi:10.1155/S0161171203210681
Modular representations of Loewy length two
Department of Mathematics, Faculty of Sciences Dhar-Mahraz, University of Sidi Mohammed Ben Abdellah, Fes BP 1796, Morocco
Received 23 October 2002
Copyright © 2003 M. E. Charkani and S. Bouhamidi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
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 J2M=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 dimK(M)=μ(M)+1, where μ(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 dimK(Rad(M))=1.