The Fitting lemma, often mentioned in the context of group theory and representation theory, primarily deals with nilpotent groups and their substructures. It provides insight into the relationship between normal subgroups and the structure of groups. Here’s a basic overview of the Fitting lemma: ### Fitting Lemma 1.
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For an endomorphism of a finite-length module , sufficiently large givesIf is indecomposable, every endomorphism is therefore either invertible or nilpotent, so its endomorphism ring is local.