Normalizers of sets of components in fusion systems

Article Sidebar

pdf (English)

Main Article Content

Bob Oliver
Université Sorbonne Paris Nord

We describe some new ways to construct saturated fusion subsystems, including, as a special case, the normalizer of a set of components of the ambient fusion system. This was motivated in part by Aschbacher’s construction of the normalizer of one component, and in part by joint work with three other authors where we had to construct the normalizer of all of the components.

Paraules clau
fusion systems, Sylow subgroups, components

Article Details

Com citar
Oliver, Bob. «Normalizers of sets of components in fusion systems». Publicacions Matemàtiques, 2023, vol.VOL 67, núm. 2, p. 795-18, http://raco.cat/index.php/PublicacionsMatematiques/article/view/418491.
Referències
M. Aschbacher, The generalized Fitting subsystem of a fusion system, Mem. Amer. Math. Soc. 209(986) (2011), 110 pp.
DOI: 10.1090/S0065-9266-2010-00621-5

M. Aschbacher, On fusion systems of component type, Mem. Amer. Math. Soc. 257(1236) (2019), 182 pp. DOI: 10.1090/memo/1236

M. Aschbacher, R. Kessar, and B. Oliver, “Fusion Systems in Algebra and Topology”, London Mathematical Society Lecture Note Series 391, Cambridge
University Press, Cambridge, 2011. DOI: 10.1017/CBO9781139003841

C. Broto, N. Castellana, J. Grodal, R. Levi, and B. Oliver, Subgroup families controlling p-local finite groups, Proc. London Math. Soc. (3) 91(2) (2005), 325–354. DOI: 10.1112/S0024611505015327

C. Broto, R. Levi, and B. Oliver, The homotopy theory of fusion systems, J. Amer. Math. Soc. 16(4) (2003), 779–856.
DOI: 10.1090/S0894-0347-03-00434-X

C. Broto, J. Møller, B. Oliver, and A. Ruiz, Realizability and tameness of fusion systems, Preprint (2021). arXiv:2102.08278v3

D. A. Craven, “The Theory of Fusion Systems. An Algebraic Approach”, Cambridge Studies in Advanced Mathematics 131, Cambridge University Press,
Cambridge, 2011. DOI: 10.1017/CBO9780511794506

D. Gorenstein, “Finite Groups”, Harper & Row, Publishers, New YorkLondon, 1968.

B. Oliver, A Krull–Remak–Schmidt theorem for fusion systems, Fund. Math. 259(3) (2022), 287–312. DOI: 10.4064/fm160-5-2022

L. Puig, Frobenius categories, J. Algebra 303(1) (2006), 309–357. DOI: 10.1016/ j.jalgebra.2006.01.023

K. Roberts and S. Shpectorov, On the definition of saturated fusion systems, J. Group Theory 12(5) (2009), 679–687. DOI: 10.1515/JGT.2009.003

R. Stancu, Equivalent definitions of fusion systems, Preprint (2004).