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All $ p$-local finite groups of rank two for odd prime $ p$

Author(s): Antonio Díaz; Albert Ruiz; Antonio Viruel
Journal: Trans. Amer. Math. Soc. 359 (2007), 1725-1764.
MSC (2000): Primary 55R35, 20D20
Posted: November 22, 2006
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Abstract: In this paper we give a classification of the rank two $ p$-local finite groups for odd $ p$. This study requires the analysis of the possible saturated fusion systems in terms of the outer automorphism group of the possible $ \mathcal{F}$-radical subgroups. Also, for each case in the classification, either we give a finite group with the corresponding fusion system or we check that it corresponds to an exotic $ p$-local finite group, getting some new examples of these for $ p=3$.

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Additional Information:

Antonio Díaz
Affiliation: Departamento de Álgebra, Geometría y Topología, Universidad de Málaga, Apdo correos 59, 29080 Málaga, Spain
Address at time of publication: Department of Mathematical Sciences, King's College, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom
Email: adiaz@agt.cie.uma.es, a.diaz@maths.abdn.ac.uk

Albert Ruiz
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Cerdanyola del Vallès, Spain
Email: Albert.Ruiz@uab.es

Antonio Viruel
Affiliation: Departamento de Álgebra, Geometría y Topología, Universidad de Málaga, Apdo correos 59, 29080 Málaga, Spain
Email: viruel@agt.cie.uma.es

DOI: 10.1090/S0002-9947-06-04367-4
PII: S 0002-9947(06)04367-4
Received by editor(s): January 25, 2005
Posted: November 22, 2006
Additional Notes: The first author was partially supported by MCED grant AP2001-2484
The second author was partially supported by MEC grant MTM2004-06686
The first and third authors were partially supported by MEC grant MTM2004-06262 and CEC-JA grant FQM213
Copyright of article: Copyright 2006, American Mathematical Society

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