Hostname: page-component-77c89778f8-swr86 Total loading time: 0 Render date: 2024-07-17T12:24:35.306Z Has data issue: false hasContentIssue false
  • English
  • Français

Splitting fusion systems over 2-groups

Part of: Representation theory of groups

Published online by Cambridge University Press:  05 December 2012

Bob Oliver
Bob Oliver*
Affiliation:
Laboratoire Analyse, Géometrie et Applications, Institut Galilée, Université Paris 13, 99 Avenue J.-B. Clément, 93430 Villetaneuse, France (bobol@math.univ-paris13.fr)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We find conditions which imply that a saturated fusion system over a product of 2-groups splits as a product of fusion systems over the factors.

Keywords

fusion systemfinite groupsautomorphisms

MSC classification

Secondary: 20D20: Sylow subgroups, Sylow properties, $pi$-groups, $pi$-structure 20C20: Modular representations and characters 20D40: Products of subgroups 20D45: Automorphisms
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 56 , Issue 1 , February 2013 , pp. 263 - 301
Copyright
Copyright © Edinburgh Mathematical Society 2012

References

1.Andersen, K., Oliver, B. and Ventura, J., Reduced, tame, and exotic fusion systems, Proc. Lond. Math. Soc. 105 (2012), 87–152.CrossRefGoogle Scholar
2.Aschbacher, M., Finite group theory (Cambridge University Press, 1986).Google Scholar
3.Aschbacher, M., Kessar, R. and Oliver, B., Fusion systems in algebra and topology (Cambridge University Press, 2011).CrossRefGoogle Scholar
4.Broto, C., Castellana, N., Grodal, J., Levi, R. and Oliver, B., Subgroup families controlling p-local finite groups, Proc. Lond. Math. Soc. 91 (2005), 325–354.CrossRefGoogle Scholar
5.Broto, C., Castellana, N., Grodal, J., Levi, R. and Oliver, B., Extensions of p-local finite groups, Trans. Am. Math. Soc. 359 (2007), 3791–3858.CrossRefGoogle Scholar
6.Broto, C., Levi, R. and Oliver, B., The homotopy theory of fusion systems, J. Am. Math. Soc. 16 (2003), 779–856.CrossRefGoogle Scholar
7.Goldschmidt, D., Strongly closed 2-subgroups of finite groups, Annals Math. 102 (1975), 475–489.CrossRefGoogle Scholar
8.Gorenstein, D., Finite groups (Harper & Row, 1968).Google Scholar
9.Gorenstein, D., Lyons, R. and Solomon, R., The classification of the finite simple groups, Volume 2, American Mathematical Society Surveys and Monographs, Volume 40 (American Mathematical Society, Providence, RI, 1996).Google Scholar
10.Oliver, B. and Ventura, J., Saturated fusion systems over 2-groups, Trans. Am. Math. Soc. 361 (2009), 6661–6728.CrossRefGoogle Scholar
11.Puig, L., Frobenius categories, J. Alg. 303 (2006), 309–357.CrossRefGoogle Scholar
12.Suzuki, M., Group theory, I (Springer, 1982).CrossRefGoogle Scholar
13.Suzuki, M., Group theory, II (Springer, 1986).CrossRefGoogle Scholar