New flag-transitive geometries for the groups \(\mathrm{Sp}_4(K)\) and \(\mathrm{SU}_5(K)\) (Q476381)
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scientific article; zbMATH DE number 6375601
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | New flag-transitive geometries for the groups \(\mathrm{Sp}_4(K)\) and \(\mathrm{SU}_5(K)\) |
scientific article; zbMATH DE number 6375601 |
Statements
New flag-transitive geometries for the groups \(\mathrm{Sp}_4(K)\) and \(\mathrm{SU}_5(K)\) (English)
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1 December 2014
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\textit{H. Pralle} and \textit{S. Shpectorov} [Adv. Geom. 7, No. 1, 1--17 (2007; Zbl 1135.51008)] described the class of ovoidal hyperplanes in dual polar spaces of rank 4. In this paper, it is observed that by removing such a hyperplane and a related second hyperplane one obtains a new geometry for the group stabilizing the ovoidal hyperplane. The authors prove that this group acts flag-transitively and that the geometry is simply connected.
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flag-transitive geometry
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polar space
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affine
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biaffine
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hyperplane
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simply connected geometry
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