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arXiv · 2501.17197

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

Morton E. Harris
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Abstract

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.

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Morton E. Harris. 2025-01-27. A Classification of the Isomorphism Types of Indecomposable and Simple Modules that Refines the Green Theory in Finite Group Modular Representation Theory. https://arxiv.org/abs/2501.17197

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