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Extensions of linking systems and fusion systems
Author(s):
Bob
Oliver
Journal:
Trans. Amer. Math. Soc.
362
(2010),
5483-5500.
MSC (2000):
Primary 55R35;
Secondary 20D20, 20E22
Posted:
May 19, 2010
MathSciNet review:
2657688
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Additional information
Abstract:
We correct two errors in the statement and proof of a theorem in an earlier paper (2007), and at the same time extend that result to a more general theorem about extensions of  -local finite groups. Other special cases of this theorem have already been shown in two later papers, so we feel it will be useful to have this more general result in the literature.
References:
-
- 1.
- K. Andersen, B. Oliver, & J. Ventura, Reduced, tame, and exotic fusion systems (preprint)
- 2.
- M. Aschbacher, Normal subsystems of fusion systems, Proc. London Math. Soc. 97 (2008), 239-271 MR 2434097
- 3.
- C. Broto, R. Levi, & B. Oliver, The homotopy theory of fusion systems, J. Amer. Math. Soc. 16 (2003), 779-856 MR 1992826 (2004k:55016)
- 4.
- C. Broto, N. Castellana, J. Grodal, R. Levi, & B. Oliver, Subgroup families controlling
 -local finite groups, Proc. London Math. Soc. 91 (2005), 325-354 MR 2167090 (2007e:20111) - 5.
- C. Broto, N. Castellana, J. Grodal, R. Levi, & B. Oliver, Extensions of
 -local finite groups, Trans. Amer. Math. Soc. 359 (2007), 3791-3858 MR 2302515 (2008i:55013) - 6.
- N. Castellana & A. Libman, Wreath products and representations of
 -local finite groups, Advances in Mathematics 221 (2009), 1302-1344. MR 2518640 (2010b:20029) - 7.
- D. Gorenstein, Finite groups, Harper & Row (1968) MR 0231903 (38:229)
- 8.
- B. Oliver & J. Ventura, Extensions of linking systems with
 -group kernel, Math. Annalen 338 (2007), 983-1043 MR 2317758 (2008k:55029) - 9.
- B. Oliver & J. Ventura, Saturated fusion systems over
 -groups, Trans. Amer. Math. Soc. 361 (2009), 6661-6728. MR 2538610 - 10.
- L. Puig, Frobenius categories, J. Algebra 303 (2006), 309-357 MR 2253665 (2007j:20011)
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Additional Information:
Bob
Oliver
Affiliation:
Laboratoire Analyse, Géométrie and Applications, Institut Galilée, Av. J-B Clément, 93430 Villetaneuse, France
Email:
bobol@math.univ-paris13.fr
DOI:
10.1090/S0002-9947-2010-05022-6
PII:
S 0002-9947(2010)05022-6
Keywords:
Classifying spaces,
Sylow subgroups,
fusion,
extensions
Received by editor(s):
November 21, 2008
Received by editor(s) in revised form:
February 13, 2009
Posted:
May 19, 2010
Additional Notes:
The author was partially supported by UMR 7539 of the CNRS
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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