Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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 $(k_{N\times N})^{G\times G}$?

share|improve this question
3  
I think you hae either forgotten some hypotheses, or written the wrong question down. The statement as it stands is false if $N = G$ and $p$ divides $|G|$ ($p$ = char($k$)). –  Geoff Robinson Sep 12 '11 at 5:00
    
I want to apply Exercise 9.6 and Lemma 9.7 to $B$. If I can show that $B$ has trivial source (as a $k(G\times G)$-module), then an indecomposable summand of $B_{N\times N}$ must have a vertex containing the intersection of $N\times N$ with a vertex of $B$, by Lemma 9.7. Exercise 9.6 says this happens, i.e. $B$ has trivial source, if $B\mid (k_{N\times N})^{G\times G}$. So it's this that I'm trying to prove. –  Clinton Boys Sep 12 '11 at 7:51
    
@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). –  Jack Schmidt Sep 25 '11 at 16:23

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.