## Extensions of $p$-local finite groups

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- by C. Broto, N. Castellana, J. Grodal, R. Levi and B. Oliver PDF
- Trans. Amer. Math. Soc.
**359**(2007), 3791-3858 Request permission

## 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.## References

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## Additional Information

**C. Broto**- Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, E–08193 Bellaterra, Spain
- MR Author ID: 42005
- 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
- MR Author ID: 191965
- Email: bob@math.univ-paris13.fr
- 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 - © Copyright 2007
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2302515