A Green ring version of the Brauer induction theorem
Let F be an algebraically closed field of prime characteristic p, let G be a finite group, let V be a fixed p-subgroup of G, and let E(V) be the set of all subgroups H of G such that \(O_ p(H)\leq V\) and \(H/O_ p(H)\) is elementary. The author shows that, in the Green ring of G, any V- projective FG-module is a \({\mathbb{Z}}\)-linear combination of modules induced from subgroups in E(V). Moreover, he proves that E(V) is in some sense minimal with this property. There are similar results with a valuation ring replacing the field F.
scientific article; zbMATH DE number 4019305