Abstract:
We first develop the necessary tools from the theory of G-algebras and endomorphism rings. Then the basic results of Green's theory of vertices and sources for kG-modules is given. Building on these, we retrace the steps of Lassueur and introduce the group of relative endo-trivial modules, which gives a generalization of the Dade group. Lastly, we introduce a related group in terms of a specific type of algebras. We describe the Jacobson radical of such algebras.
