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Existence and uniqueness of classifying spaces for fusion systems over discrete p ‐toral groups
Author(s) -
Levi Ran,
Libman Assaf
Publication year - 2015
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdu062
Subject(s) - uniqueness , context (archaeology) , mathematics , group (periodic table) , group theory , pure mathematics , algebra over a field , discrete mathematics , mathematical analysis , geography , physics , archaeology , quantum mechanics
A major question 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 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 generalize 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.