Extensions of -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 | References | Similar Articles | 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:
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.