Ree geometries
Copyright policy )Ree geometries
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.
- Ghent University Belgium
Moufang set, unital, Moufang sets, Ree hexagon, Group Theory (math.GR), 51E12, Ree groups, FOS: Mathematics, Mathematics - Combinatorics, polarity, ovoid, 20B25, Ree unital, Finite automorphism groups of algebraic, geometric, or combinatorial structures, collineation group, General block designs in finite geometry, Ree group, Mathematics and Statistics, 20B25; 51E05; 51E12, 51E05, mixed hexagons, Combinatorics (math.CO), Generalized quadrangles and generalized polygons in finite geometry, Mathematics - Group Theory
Moufang set, unital, Moufang sets, Ree hexagon, Group Theory (math.GR), 51E12, Ree groups, FOS: Mathematics, Mathematics - Combinatorics, polarity, ovoid, 20B25, Ree unital, Finite automorphism groups of algebraic, geometric, or combinatorial structures, collineation group, General block designs in finite geometry, Ree group, Mathematics and Statistics, 20B25; 51E05; 51E12, 51E05, mixed hexagons, Combinatorics (math.CO), Generalized quadrangles and generalized polygons in finite geometry, Mathematics - Group Theory
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