Subcentric linking systems

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We propose a definition of a linking system which is slightly more general than the one currently in the literature. Whereas the objects of linking systems in the current definition are always quasicentric, the objects of our linking systems only need to satisfy a weaker condition. This leads to the definition of subcentric subgroups of fusion systems. We prove that there is a unique linking system associated to each fusion system whose objects are the subcentric subgroups. Furthermore, the nerve of such a subcentric linking system is homotopy equivalent to the nerve of the centric linking system. The existence of subcentric linking systems seems to be of interest for a classification of fusion systems of characteristic $p$-type. The various results we prove about subcentric subgroups indicate furthermore that the concept is of interest for studying extensions of linking system and fusion systems.
Original languageEnglish
Pages (from-to)3325-3373
Number of pages38
JournalTransactions of the American Mathematical Society
Issue number5
Early online date26 Oct 2018
Publication statusPublished - 2019



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