In mathematics, **Maschke's theorem**, named after Heinrich Maschke, is a theorem in group representation theory that concerns the decomposition of representations of a finite group into irreducible pieces. If (*V*, *ρ*) is a finite-dimensional representation of a finite group *G* over a field of characteristic zero, and *U* is an invariant subspace of *V*, then the theorem claims that *U* admits an invariant direct complement *W*; in other words, the representation (*V*, *ρ*) is completely reducible. More generally, the theorem holds for fields of positive characteristic *p*, such as the finite fields, if the prime *p* doesn't divide the order of *G.*

Read more about Maschke's Theorem: Reformulation and The Meaning

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**Maschke's Theorem**- Reformulation and The Meaning

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**Maschke's theorem**addresses the question is a general (finite-dimensional) representation built from irreducible subrepresentations using the direct sum operation? In the module-theoretic language ... well developed theory of semisimple rings, in particular, the Artin–Wedderburn

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### Famous quotes containing the word theorem:

“To insure the adoration of a *theorem* for any length of time, faith is not enough, a police force is needed as well.”

—Albert Camus (1913–1960)