Fusion systems and localities -- a dictionary

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Abstract

Linking systems were introduced to provide algebraic models for p-completed classifying spaces of fusion systems. Every linking system over a saturated fusion system F corresponds to a group-like structure called a locality. Given such a locality L, we prove that there is a one-to-one correspondence between the partial normal subgroups of L and the normal subsystems of the fusion system F. This is then used to obtain a kind of dictionary, which makes it possible to translate between various concepts in localities and corresponding concepts in fusion systems. As a byproduct, we obtain new proofs of many known theorems about fusion systems and also some new results. For example, we show in this paper that, in any saturated fusion system, there is a sensible notion of a product of normal subsystems.

Details

Original languageEnglish
Article number108690
Pages (from-to)1-92
Number of pages92
JournalAdvances in Mathematics
Volume410
Issue numberPart A
Publication statusPublished - 3 Dec 2022
Peer-reviewedYes

External IDs

Scopus 85138131666

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