Fusion systems and localities -- a dictionary
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Contributors
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 language | English |
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Article number | 108690 |
Pages (from-to) | 1-92 |
Number of pages | 92 |
Journal | Advances in Mathematics |
Volume | 410 |
Issue number | Part A |
Publication status | Published - 3 Dec 2022 |
Peer-reviewed | Yes |
External IDs
Scopus | 85138131666 |
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