Extensions of linking systems and fusion systems
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- by Bob Oliver PDF
- Trans. Amer. Math. Soc. 362 (2010), 5483-5500 Request permission
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 $p$-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
- K. Andersen, B. Oliver, & J. Ventura, Reduced, tame, and exotic fusion systems (preprint)
- Michael Aschbacher, Normal subsystems of fusion systems, Proc. Lond. Math. Soc. (3) 97 (2008), no. 1, 239–271. MR 2434097, DOI 10.1112/plms/pdm057
- Carles Broto, Ran Levi, and Bob Oliver, The homotopy theory of fusion systems, J. Amer. Math. Soc. 16 (2003), no. 4, 779–856. MR 1992826, DOI 10.1090/S0894-0347-03-00434-X
- Carles Broto, Natàlia Castellana, Jesper Grodal, Ran Levi, and Bob Oliver, Subgroup families controlling $p$-local finite groups, Proc. London Math. Soc. (3) 91 (2005), no. 2, 325–354. MR 2167090, DOI 10.1112/S0024611505015327
- C. Broto, N. Castellana, J. Grodal, R. Levi, and B. Oliver, Extensions of $p$-local finite groups, Trans. Amer. Math. Soc. 359 (2007), no. 8, 3791–3858. MR 2302515, DOI 10.1090/S0002-9947-07-04225-0
- Natàlia Castellana and Assaf Libman, Wreath products and representations of $p$-local finite groups, Adv. Math. 221 (2009), no. 4, 1302–1344. MR 2518640, DOI 10.1016/j.aim.2009.02.011
- Daniel Gorenstein, Finite groups, Harper & Row, Publishers, New York-London, 1968. MR 0231903
- Bob Oliver and Joana Ventura, Extensions of linking systems with $p$-group kernel, Math. Ann. 338 (2007), no. 4, 983–1043. MR 2317758, DOI 10.1007/s00208-007-0104-4
- Bob Oliver and Joana Ventura, Saturated fusion systems over 2-groups, Trans. Amer. Math. Soc. 361 (2009), no. 12, 6661–6728. MR 2538610, DOI 10.1090/S0002-9947-09-04881-8
- Lluis Puig, Frobenius categories, J. Algebra 303 (2006), no. 1, 309–357. MR 2253665, DOI 10.1016/j.jalgebra.2006.01.023
Additional Information
- Bob Oliver
- Affiliation: Laboratoire Analyse, Géométrie and Applications, Institut Galilée, Av. J-B Clément, 93430 Villetaneuse, France
- MR Author ID: 191965
- Email: bobol@math.univ-paris13.fr
- Received by editor(s): November 21, 2008
- Received by editor(s) in revised form: February 13, 2009
- Published electronically: May 19, 2010
- Additional Notes: The author was partially supported by UMR 7539 of the CNRS
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 362 (2010), 5483-5500
- MSC (2000): Primary 55R35; Secondary 20D20, 20E22
- DOI: https://doi.org/10.1090/S0002-9947-2010-05022-6
- MathSciNet review: 2657688