Modular representations of Loewy length two - M. E. Charkani; S. Bouhamidi (International Journal of Mathematics and Mathematical Sciences)
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.