Hostname: page-component-7b7567c8c-wxvwp Total loading time: 0 Render date: 2026-11-15T14:10:15.298Z Has data issue: false hasContentIssue false
  • English
  • Français

The norm of a Ree group

Published online by Cambridge University Press:  11 January 2016

Tom De Medts and
Richard M. Weiss
Tom De Medts
Affiliation:
Department of Mathematics, Ghent University, Krijgslaan 281, S22, 9000 Gent, Belgium, tdemedts@cage.ugent.be
Richard M. Weiss
Affiliation:
Department of Mathematics, Tufts University, Medford, Massachusetts 02155, USA, rweiss@tufts.edu
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 give an explicit construction of the Ree groups of type G 2 as groups acting on mixed Moufang hexagons together with detailed proofs of the basic properties of these groups contained in the two fundamental papers of Tits on this subject (see [7] and [8]). We also give a short proof that the norm of a Ree group is anisotropic.

Keywords

20E4251E1251E24

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 199 , September 2010, pp. 15 - 41
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2010

References

[1] De Medts, T. and Weiss, R. M., Moufang sets and Jordan division algebras, Math. Ann. 335 (2006), 415–433.Google Scholar
[2] Guralnick, R. M., Kantor, W. M., Kassabov, M., and Lubotzky, A., Presentations of finite simple groups: A quantitative approach, J. Amer. Math. Soc. 21 (2008), 711–774.CrossRefGoogle Scholar
[3] Hitzelberger, P., Kramer, L., and Weiss, R. M., Non-discrete Euclidean buildings for the Ree and Suzuki groups, to appear in Amer. J. Math., preprint, arXiv:math/0810.2725 [math.GR]Google Scholar
[4] Kemper, G., Lübeck, F., and Magaard, K., Matrix generators for the Ree groups 2G2(q), Comm. Algebra 29 (2001), 407–413.Google Scholar
[5] Ree, R., A family of simple groups associated with the simple Lie algebra of type (G2), Amer. J. Math. 83 (1961), 432–462.CrossRefGoogle Scholar
[6] Tits, J., Algebraic and abstract simple groups, Ann. Math. 80 (1964), 313–329.Google Scholar
[7] Tits, J., Moufang octagons and Ree groups of type F4 , Amer. J. Math. 105 (1983), 539–594.CrossRefGoogle Scholar
[8] Tits, J., “Les groupes simples de Suzuki et de Ree” in Séminaire Bourbaki, Vol. 6 (1960/1961), no. 210, Soc. Math. France, Paris, 1995, 65–82.Google Scholar
[9] Tits, J. and Weiss, R. M., Moufang Polygons, Springer, Berlin, 2002.CrossRefGoogle Scholar
[10] Van Maldeghem, H., Generalized Polygons, Birkhäuser, Basel, 1998.Google Scholar