On saturated fusion systems and Brauer indecomposability of Scott modules

Details On saturated fusion systems and Brauer indecomposability of Scott modules On saturated fusion systems and Brauer indecomposability of Scott modules

2010-09-13

arxiv.org/abs/1009.2391v1

Mathematics

Representation Theory

Scientific paper

Let $p$ be a prime number, $G$ a finite group, $P$ a $p$-subgroup of $G$ and $k$ an algebraically closed field of characteristic $p$. We study the relationship between the category $\Ff_P(G)$ and the behavior of $p$-permutation $kG$-modules with vertex $P$ under the Brauer construction. We give a sufficient condition for $\Ff_P(G)$ to be a saturated fusion system. We prove that for Scott modules with abelian vertex, our condition is also necessary. In order to obtain our results, we prove a criterion for the categories arising from the data of $(b, G)$-Brauer pairs in the sense of Alperin-Brou\'e and Brou\'e-Puig to be saturated fusion systems on the underlying $p$-group.

Affiliated with

Also associated with

No associations

Rating

On saturated fusion systems and Brauer indecomposability of Scott modules does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On saturated fusion systems and Brauer indecomposability of Scott modules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On saturated fusion systems and Brauer indecomposability of Scott modules will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-337684