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Ree geometries

Fabienne Haot, Koen Struyve (UGent) and Hendrik Van Maldeghem (UGent)
(2011) FORUM MATHEMATICUM. 23(1). p.75-98
Author
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Abstract
We introduce a rank 3 geometry for any Ree group over a not necessarily perfect field and show that its full collineation group is the automorphism group of the corresponding Ree group. A similar result holds for two rank 2 geometries obtained as a truncation of this rank 3 geometry. As an application, we show that a polarity in any Moufang generalized hexagon is unambiguously determined by its set of absolute points, or equivalently, its set of absolute lines.
Keywords
Moufang sets, Ree groups, Ree unital, mixed hexagons

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Citation

Please use this url to cite or link to this publication:

Chicago
Haot, Fabienne, Koen Struyve, and Hendrik Van Maldeghem. 2011. “Ree Geometries.” Forum Mathematicum 23 (1): 75–98.
APA
Haot, F., Struyve, K., & Van Maldeghem, H. (2011). Ree geometries. FORUM MATHEMATICUM, 23(1), 75–98.
Vancouver
1.
Haot F, Struyve K, Van Maldeghem H. Ree geometries. FORUM MATHEMATICUM. 2011;23(1):75–98.
MLA
Haot, Fabienne, Koen Struyve, and Hendrik Van Maldeghem. “Ree Geometries.” FORUM MATHEMATICUM 23.1 (2011): 75–98. Print.
@article{1199274,
  abstract     = {We introduce a rank 3 geometry for any Ree group over a not necessarily perfect field and show that its full collineation group is the automorphism group of the corresponding Ree group. A similar result holds for two rank 2 geometries obtained as a truncation of this rank 3 geometry. As an application, we show that a polarity in any Moufang generalized hexagon is unambiguously determined by its set of absolute points, or equivalently, its set of absolute lines.},
  author       = {Haot, Fabienne and Struyve, Koen and Van Maldeghem, Hendrik},
  issn         = {0933-7741},
  journal      = {FORUM MATHEMATICUM},
  keyword      = {Moufang sets,Ree groups,Ree unital,mixed hexagons},
  language     = {eng},
  number       = {1},
  pages        = {75--98},
  title        = {Ree geometries},
  url          = {http://dx.doi.org/10.1515/FORM.2011.002},
  volume       = {23},
  year         = {2011},
}
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