Minimal characteristic bisets for fusion systems

2014/03/26 by Matthew Gelvin, Gelvin, Matthew, Sune Precht Reeh +1
Mathematics · #19A22) #20D20 (20J15 #Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #math.AT #math.GR #math.RT #msc:20D20

paper · pdf · doi:10.48550/arxiv.1403.6884

26 pages

arxiv created 2014/03/26 · arxiv updated 2014/03/28

Abstract

We show that every saturated fusion system F has a unique minimal F-characteristic biset Λ_F. We examine the relationship of Λ_F with other concepts in p-local finite group theory: In the case of a constrained fusion system, the model for the fusion system is the minimal F-characteristic biset, and more generally, any centric linking system can be identified with the F-centric part of Λ_F as bisets. We explore the grouplike properties of Λ_F, and conjecture an identification of normalizer subsystems of F with subbisets of Λ_F.

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