Saturated fusion systems over 2-groups

We develop methods for listing, for a given 2-group S, all nonconstrained centerfree saturated fusion systems over S. These are the saturated fusion systems which could, potentially, include minimal examples of exotic fusion systems: fusion systems not arising from any finite group. To test our meth...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2009-12, Vol.361 (12), p.6661-6728
Main Authors: OLIVER, BOB, VENTURA, JOANA
Format: Article
Language:English
Subjects:
Algebra
Automorphisms
Commutators
Eigenvalues
Exact sciences and technology
Group theory
Group theory and generalizations
Homomorphisms
Mathematics
Matrices
Morphisms
Quaternions
Sciences and techniques of general use
Vector spaces
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Summary:We develop methods for listing, for a given 2-group S, all nonconstrained centerfree saturated fusion systems over S. These are the saturated fusion systems which could, potentially, include minimal examples of exotic fusion systems: fusion systems not arising from any finite group. To test our methods, we carry out this program over four concrete examples: two of order 2^7 and two of order 2^{10}. Our long term goal is to make a wider, more systematic search for exotic fusion systems over 2-groups of small order.
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-09-04881-8