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Extensions of  -local finite groups
Author(s):
C.
Broto;
N.
Castellana;
J.
Grodal;
R.
Levi;
B.
Oliver
Journal:
Trans. Amer. Math. Soc.
359
(2007),
3791-3858.
MSC (2000):
Primary 55R35;
Secondary 55R40, 20D20
Posted:
March 20, 2007
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Additional information
Abstract:
A  -local finite group consists of a finite  -group  , together with a pair of categories which encode ``conjugacy'' relations among subgroups of  , and which are modelled on the fusion in a Sylow  -subgroup of a finite group. It contains enough information to define a classifying space which has many of the same properties as  -completed classifying spaces of finite groups. In this paper, we study and classify extensions of  -local finite groups, and also compute the fundamental group of the classifying space of a  -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:
10.1090/S0002-9947-07-04225-0
PII:
S 0002-9947(07)04225-0
Keywords:
Classifying space,
$p$-completion,
finite groups,
fusion.
Received by editor(s):
July 11, 2005
Posted:
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
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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