High Quality Content by WIKIPEDIA articles! Maschke's theorem is a theorem in group representation theory which concerns the decomposition of representations of a finite group into irreducible pieces. If (V, ) 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, ) 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. It is named after Heinrich Maschke.

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