2019/09/27 by Jamison Barsotti, Barsotti, Jamison, Rob Carman +1
Chemistry · Mathematics · Biochemistry, Genetics and Molecular Biology · #Carbohydrate Chemistry and Synthesis #Finite Group Theory Research #Ubiquitin and proteasome pathways
paper · pdf · doi:10.48550/arxiv.1909.12783
For a saturated fusion system \mathcal F on a p-group S, we study the Burnside ring of the fusion system B(\mathcal F), as defined by Matthew Gelvin and Sune Reeh, which is a subring of the Burnside ring B(S). We give criteria for an element of B(S) to be in B(\mathcal F) determined by the \mathcal F-automorphism groups of essential subgroups of S. When \mathcal F is the fusion system induced by a finite group G with S as a Sylow p-group, we show that the restriction of B(G) to B(S) has image equal to B(\mathcal F). We also show that for p=2, we can gain information about the fusion system by studying the unit group B(\mathcal F)^×. When S is abelian, we completely determine this unit group.