A Classification of the Isomorphism Types of Indecomposable and Simple Modules that Refines the Green Theory in Finite Group Modular Representation Theory

In Finite Group Modular Representation Theory, the basic objects are the indecomposable and simple modules. This paper offers a new classification of these objects that refines the Green Theory Classification of indecomposable and simple modules. The sets of isomorphism tyes of these modules is decomposed into disjoint, non-empty subsets such that any two elements in any subset share Green Theory Invariants. We also prove a new formula for the number of isomorphism types of absolutely simple modules of finite groups in prime characteristic.