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Representations and Characters of Groups, Second Edition by Martin Liebeck, Gordon James

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11

More on the group algebra

We now go further into the structure of the group algebra imageG of a finite group G. As in Chapter 10, we write

image

a direct sum of irreducible imageG-modules Ui. In Theorem 10.5 we proved that every irreducible imageG-module U is isomorphic to one of the Ui. The question arises: how many of the Ui are isomorphic to U? There is an elegant ...

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