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Maschke's Theorem

If a Matrix Group is reducible, then it is completely reducible, i.e., if the Matrix Group is equivalent to the Matrix Group in which every Matrix has the reduced form

\begin{displaymath}
\left[{\matrix{D_i^{(1)} & X_i\cr 0 & D_i^{(2)}\cr}}\right],
\end{displaymath}

then it is equivalent to the Matrix Group obtained by putting $X_i=0$.

See also Matrix Group


References

Lomont, J. S. Applications of Finite Groups. New York: Dover, p. 49, 1987.




© 1996-9 Eric W. Weisstein
1999-05-26