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International Journal of Mathematics and Mathematical Sciences
Volume 2003, Issue 70, Pages 4399-4408

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 Hindawi Publishing Corporation. 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.


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.