A Krull–Remak–Schmidt theorem for fusion systems
Volume 259 / 2022
Fundamenta Mathematicae 259 (2022), 287-312
MSC: Primary 20D20; Secondary 20D40, 20D45.
DOI: 10.4064/fm160-5-2022
Published online: 8 August 2022
Abstract
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.
