Realizability of fusion systems by discrete groups: II

2025/05/22 by Broto, Carles, Levi, Ran, Oliver, Bob
#20D20 #20F50 #Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2505.16375

Abstract

We compare four different types of realizability for saturated fusion systems over discrete p-toral groups. For example, when G is a locally finite group all of whose p-subgroups are artinian (hence discrete p-toral), we show that it has ``weakly Sylow'' p-subgroups and give explicit constructions of saturated fusion systems and associated linking systems associated to G. We also show that a fusion system over a discrete p-toral group S is saturated if its set of morphisms is closed under a certain topology and the finite subgroups of S satisfy the saturation axioms, and prove a version of the Cartan-Eilenberg stable elements theorem for locally finite groups.

Citations

• Limits over orbit categories of locally finite groups
• Realizability of fusion systems by discrete groups

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• Fusion systems over a Sylow p-subgroup of G₂(p)