Modular representations of Loewy length two.
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 \(\dim_K(\text{Rad}(M))=1\).
scientific article; zbMATH DE number 2166341