Existence and uniqueness of classifying spaces for fusion systems over discrete p-toral groups

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Abstract

A major questions in the theory of p-local finite groups was whether any saturated fusion system over a finite p-group admits an associated centric linking system, and when it does, whether it is unique. Both questions were answered in the affirmative by A. Chermak, using the theory of partial groups and localities he developed. Using Chermak’s ideas combined with the techniques of obstruction theory, Bob Oliver gave a different proof of Chermak’s theorem. In this paper we generalise Oliver’s proof to the context of fusion systems over discrete p-toral groups, thus positively resolving the analogous questions in p-local compact group theory.
Original languageEnglish
Pages (from-to)47-70
Number of pages24
JournalJournal of the London Mathematical Society
Volume91
Issue number1
Early online date17 Nov 2014
DOIs
Publication statusPublished - Feb 2015

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Classifying Space
P-groups
Fusion
Existence and Uniqueness
Obstruction Theory
Finite P-group
Compact Group
Group Theory
Locality
Linking
Finite Group
Partial
Generalise
Theorem

Cite this

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title = "Existence and uniqueness of classifying spaces for fusion systems over discrete p-toral groups",
abstract = "A major questions in the theory of p-local finite groups was whether any saturated fusion system over a finite p-group admits an associated centric linking system, and when it does, whether it is unique. Both questions were answered in the affirmative by A. Chermak, using the theory of partial groups and localities he developed. Using Chermak’s ideas combined with the techniques of obstruction theory, Bob Oliver gave a different proof of Chermak’s theorem. In this paper we generalise Oliver’s proof to the context of fusion systems over discrete p-toral groups, thus positively resolving the analogous questions in p-local compact group theory.",
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AB - A major questions in the theory of p-local finite groups was whether any saturated fusion system over a finite p-group admits an associated centric linking system, and when it does, whether it is unique. Both questions were answered in the affirmative by A. Chermak, using the theory of partial groups and localities he developed. Using Chermak’s ideas combined with the techniques of obstruction theory, Bob Oliver gave a different proof of Chermak’s theorem. In this paper we generalise Oliver’s proof to the context of fusion systems over discrete p-toral groups, thus positively resolving the analogous questions in p-local compact group theory.

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