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 FP(G) and the behavior of p-permutation kG-modules with vertex P under the Brauer construction. We give a sufficient condition for FP(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 give a criterion for the categories arising 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.
Original language | English |
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Pages (from-to) | 90-103 |
Number of pages | 14 |
Journal | Journal of Algebra |
Volume | 340 |
Issue number | 1 |
Early online date | 8 Jun 2011 |
DOIs | |
Publication status | Published - 15 Aug 2011 |
Keywords
- representations of finite groups
- fusion systems
- saturated triples
- Scott modules