A new family of extended generalized quadrangles
For every hyperovalOofPG(2,q) (qeven), we construct an extended generalized quadrangle with point-residues isomorphic to the generalized quadrangleT*2(O) of order(q-1, q+1).These extended generalized quadrangles are flag-transitive only whenq=2 or 4. Whenq=2 we obtain a thin-lined polar space with f...
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| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2013
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| Online Access: | https://hdl.handle.net/10356/95391 http://hdl.handle.net/10220/9281 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | For every hyperovalOofPG(2,q) (qeven), we construct an extended generalized quadrangle with point-residues isomorphic to the generalized quadrangleT*2(O) of order(q-1, q+1).These extended generalized quadrangles are flag-transitive only whenq=2 or 4. Whenq=2 we obtain a thin-lined polar space with four planes on every line. Whenq=4 we obtain one of the geometries discovered by Yoshiara [28]. That geometry is produced in [28] as a quotient of another one, which is simply connected, constructed in [28] by amalgamation of parabolics. In this paper we also give a ‘topological’ construction of that simply connected geometry. |
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