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A classification of transitive ovoids, spreads, and m -systems of polar spaces

A classification of transitive ovoids, spreads, and m -systems of polar spaces Many of the known ovoids and spreads of finite polar spaces admit a transitive group of collineations, and in 1988, P. Kleidman classified the ovoids admitting a 2-transitive group. A. Gunawardena has recently extended this classification by determining the ovoids of the seven-dimensional hyperbolic quadric which admit a primitive group. In this paper we classify the ovoids and spreads of finite polar spaces which are stabilised by an insoluble transitive group of collineations, as a corollary of a more general classification of m -systems admitting such groups. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

A classification of transitive ovoids, spreads, and m -systems of polar spaces

Forum Mathematicum , Volume 21 (2) – Mar 1, 2009

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References (57)

Publisher
de Gruyter
Copyright
© de Gruyter 2009
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/FORUM.2009.010
Publisher site
See Article on Publisher Site

Abstract

Many of the known ovoids and spreads of finite polar spaces admit a transitive group of collineations, and in 1988, P. Kleidman classified the ovoids admitting a 2-transitive group. A. Gunawardena has recently extended this classification by determining the ovoids of the seven-dimensional hyperbolic quadric which admit a primitive group. In this paper we classify the ovoids and spreads of finite polar spaces which are stabilised by an insoluble transitive group of collineations, as a corollary of a more general classification of m -systems admitting such groups.

Journal

Forum Mathematicumde Gruyter

Published: Mar 1, 2009

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