Fusion systems on small -groups

In this article we study several classes of ‘small’ 2 2 -groups: we complete the classification, started by Stancu, of all saturated fusion systems on metacyclic p p -groups for all primes p p . We consider Suzuki 2 2 -groups, and classify all center-free saturated fusion systems on 2 2 -groups of 2...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2012-11, Vol.364 (11), p.5945-5967
Main Authors: Craven, David, Glesser, Adam
Format: Article
Language:English
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Summary:In this article we study several classes of ‘small’ 2 2 -groups: we complete the classification, started by Stancu, of all saturated fusion systems on metacyclic p p -groups for all primes p p . We consider Suzuki 2 2 -groups, and classify all center-free saturated fusion systems on 2 2 -groups of 2 2 -rank 2 2 . We end by classifying all possible F \mathcal {F} -centric, F \mathcal {F} -radical subgroups in saturated fusion systems on 2 2 -groups of 2 2 -rank 2 2 .
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-2012-05580-2