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A Krull–Remak–Schmidt theorem for fusion systems

Volume 259 / 2022

Bob Oliver Fundamenta Mathematicae 259 (2022), 287-312 MSC: Primary 20D20; Secondary 20D40, 20D45. DOI: 10.4064/fm160-5-2022 Published online: 8 August 2022


We prove that the factorization of a saturated fusion system over a discrete $p$-toral group as a product of indecomposable subsystems is unique up to normal automorphisms of the fusion system and permutations of the factors. In particular, if the fusion system has trivial center, or if its focal subgroup is the entire Sylow group, then this factorization is unique (up to the ordering of the factors). This result was motivated by questions about automorphism groups of products of fusion systems.


  • Bob OliverUniversité Sorbonne Paris Nord
    LAGA, UMR 7539 du CNRS
    99, Av. J.-B. Clément
    93430 Villetaneuse, France

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