On saturated fusion systems and Brauer indecomposability of Scott modules

Kessar, R., Kunugi, N. & Mitsuhashi, N. (2011). On saturated fusion systems and Brauer indecomposability of Scott modules. Journal of Algebra, 340(1), pp. 90-103. doi: 10.1016/j.jalgebra.2011.04.029

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Abstract

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.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: School of Engineering & Mathematical Sciences > Department of Mathematical Science
Related URLs:
URI: http://openaccess.city.ac.uk/id/eprint/1896

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