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Extensions of $ p$-local finite groups


Authors: C. Broto, N. Castellana, J. Grodal, R. Levi and B. Oliver
Journal: Trans. Amer. Math. Soc. 359 (2007), 3791-3858
MSC (2000): Primary 55R35; Secondary 55R40, 20D20
DOI: https://doi.org/10.1090/S0002-9947-07-04225-0
Published electronically: March 20, 2007
MathSciNet review: 2302515
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Abstract: A $ p$-local finite group consists of a finite $ p$-group $ S$, together with a pair of categories which encode ``conjugacy'' relations among subgroups of $ S$, and which are modelled on the fusion in a Sylow $ p$-subgroup of a finite group. It contains enough information to define a classifying space which has many of the same properties as $ p$-completed classifying spaces of finite groups. In this paper, we study and classify extensions of $ p$-local finite groups, and also compute the fundamental group of the classifying space of a $ p$-local finite group.


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Additional Information

C. Broto
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, E–08193 Bellaterra, Spain
Email: broto@mat.uab.es

N. Castellana
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, E–08193 Bellaterra, Spain
Email: natalia@mat.uab.es

J. Grodal
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
Address at time of publication: Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 København Ø, Denmark
Email: jg@math.uchicago.edu, jg@math.ku.dk

R. Levi
Affiliation: Department of Mathematical Sciences, University of Aberdeen, Meston Building 339, Aberdeen AB24 3UE, United Kingdom
Email: ran@maths.abdn.ac.uk

B. Oliver
Affiliation: LAGA, Institut Galilée, Av. J-B Clément, 93430 Villetaneuse, France
Email: bob@math.univ-paris13.fr

DOI: https://doi.org/10.1090/S0002-9947-07-04225-0
Keywords: Classifying space, $p$-completion, finite groups, fusion.
Received by editor(s): July 11, 2005
Published electronically: March 20, 2007
Additional Notes: The first author was partially supported by MCYT grant BFM2001–2035
The second author was partially supported by MCYT grant BFM2001–2035
The third author was partially supported by NSF grants DMS-0104318 and DMS-0354633
The fourth author was partially supported by EPSRC grant GR/M7831.
The fifth author was partially supported by UMR 7539 of the CNRS
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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