On saturated fusion systems and Brauer indecomposability of Scott modules [article]

Radha Kessar, Naoko Kunugi, Naofumi Mitsuhashi
2010 arXiv   pre-print
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 _P(G) and the behavior of p-permutation kG-modules with vertex P under the Brauer construction. We give a sufficient condition for _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
more » ... ng from the data of (b, G)-Brauer pairs in the sense of Alperin-Broué and Broué-Puig to be saturated fusion systems on the underlying p-group.
arXiv:1009.2391v1 fatcat:llx247sxzvbmlkvi35cayztj4i