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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Fusion systems on small $ p$-groups


Authors: David A. Craven and Adam Glesser
Journal: Trans. Amer. Math. Soc. 364 (2012), 5945-5967
MSC (2010): Primary 20D20; Secondary 20D45
Published electronically: May 24, 2012
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Abstract: In this article we study several classes of `small' $ 2$-groups: we complete the classification, started by Stancu, of all saturated fusion systems on metacyclic $ p$-groups for all primes $ p$. We consider Suzuki $ 2$-groups, and classify all center-free saturated fusion systems on $ 2$-groups of $ 2$-rank $ 2$. We end by classifying all possible $ \mathcal {F}$-centric, $ \mathcal {F}$-radical subgroups in saturated fusion systems on $ 2$-groups of $ 2$-rank $ 2$.


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Additional Information

David A. Craven
Affiliation: School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom
Email: d.a.craven@bham.ac.uk

Adam Glesser
Affiliation: Department of Mathematics, California State University Fullerton, Fullerton, California 92834

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05580-2
PII: S 0002-9947(2012)05580-2
Received by editor(s): July 9, 2010
Received by editor(s) in revised form: February 25, 2011
Published electronically: May 24, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.