Local sharply transitive actions on finite generalized quadrangles
- Author
- Theo Gründhofer and Hendrik Van Maldeghem (UGent)
- Organization
- Abstract
- We classify the finite generalized quadrangles containing a line L such that some group of collineations acts sharply transitively on the ordered pentagons which start with two points of L. This can be seen as a generalization of a result of Thas and the second author [22] classifying all finite generalized quadrangles admitting a collineation group that acts transitively on all ordered pentagons, although the restriction to sharp transitivity is essential in our arguments. However, the conclusion is exactly the same family of classical generalized quadrangles (the orthogonal quadrangles and their duals). Our main result thus provides a local group theoretic characterization of these classical quadrangles.
- Keywords
- POLYGONS, PLANES, classical generalized quadrangles, root elations, Moufang panel, HOMOGENEITY, CLASSIFICATION
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-2471800
- MLA
- Gründhofer, Theo, and Hendrik Van Maldeghem. “Local Sharply Transitive Actions on Finite Generalized Quadrangles.” ANNALS OF COMBINATORICS, vol. 15, no. 1, 2011, pp. 69–80, doi:10.1007/s00026-011-0083-8.
- APA
- Gründhofer, T., & Van Maldeghem, H. (2011). Local sharply transitive actions on finite generalized quadrangles. ANNALS OF COMBINATORICS, 15(1), 69–80. https://doi.org/10.1007/s00026-011-0083-8
- Chicago author-date
- Gründhofer, Theo, and Hendrik Van Maldeghem. 2011. “Local Sharply Transitive Actions on Finite Generalized Quadrangles.” ANNALS OF COMBINATORICS 15 (1): 69–80. https://doi.org/10.1007/s00026-011-0083-8.
- Chicago author-date (all authors)
- Gründhofer, Theo, and Hendrik Van Maldeghem. 2011. “Local Sharply Transitive Actions on Finite Generalized Quadrangles.” ANNALS OF COMBINATORICS 15 (1): 69–80. doi:10.1007/s00026-011-0083-8.
- Vancouver
- 1.Gründhofer T, Van Maldeghem H. Local sharply transitive actions on finite generalized quadrangles. ANNALS OF COMBINATORICS. 2011;15(1):69–80.
- IEEE
- [1]T. Gründhofer and H. Van Maldeghem, “Local sharply transitive actions on finite generalized quadrangles,” ANNALS OF COMBINATORICS, vol. 15, no. 1, pp. 69–80, 2011.
@article{2471800,
abstract = {{We classify the finite generalized quadrangles containing a line L such that some group of collineations acts sharply transitively on the ordered pentagons which start with two points of L. This can be seen as a generalization of a result of Thas and the second author [22] classifying all finite generalized quadrangles admitting a collineation group that acts transitively on all ordered pentagons, although the restriction to sharp transitivity is essential in our arguments. However, the conclusion is exactly the same family of classical generalized quadrangles (the orthogonal quadrangles and their duals). Our main result thus provides a local group theoretic characterization of these classical quadrangles.}},
author = {{Gründhofer, Theo and Van Maldeghem, Hendrik}},
issn = {{0218-0006}},
journal = {{ANNALS OF COMBINATORICS}},
keywords = {{POLYGONS,PLANES,classical generalized quadrangles,root elations,Moufang panel,HOMOGENEITY,CLASSIFICATION}},
language = {{eng}},
number = {{1}},
pages = {{69--80}},
title = {{Local sharply transitive actions on finite generalized quadrangles}},
url = {{http://doi.org/10.1007/s00026-011-0083-8}},
volume = {{15}},
year = {{2011}},
}
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