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I have a question relating to p109 of Local representation theory by JL Alperin.

Let $G$ be a finite group and let $N$ be a normal subgroup. If $B$ is a block of $G$, why must $B$ be a summand of $(k_{N\times N})^{G\times G}$?

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    @Clinton: I don't see how to interpret that line of the proof other than how you did, but how you did is definitely wrong. You should rephrase this question (and answer it if you know the answer!) so that it more specifically addresses your question: how can you use Lemma 9.7 and exercise 9.6 in this situation (since the hypotheses are not satisfied).2011-09-25

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