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A classification of transitive ovoids, spreads, and m-systems of polar spaces
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John Bamberg
Published/Copyright:
March 12, 2009
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.
Received: 2007-06-22
Published Online: 2009-03-12
Published in Print: 2009-March
© de Gruyter 2009
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Articles in the same Issue
- Homotopy theory of small diagrams over large categories
- A classification of transitive ovoids, spreads, and m-systems of polar spaces
- Frobenius complements of exponent dividing 2m · 9
- Asymptotics of class numbers for progressions and for fundamental discriminants
- A difference characterization of Besov and Triebel-Lizorkin spaces on RD-spaces
- A topological version of the Bergman property
- A unified treatment of certain majorization results on eigenvalues and singular values of matrices
- Finite index subgroups of conjugacy separable groups
- A Bohr-like compactification and summability of Fourier series
