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On the transitivity of the orthogonal and symplectic groups in projective space

Published online by Cambridge University Press:  24 October 2008

R. H. Dye
Affiliation:
University of Newcastle upon Tyne

Extract

1. Introduction. Let Ω be a non-singular quadric in an n-dimensional projective space PG(n, K) whose coordinate field is K. With respect to Ω the linear subspaces of PG(n, K) fall into various types: the subspaces of a given type each have the same dimension and the same geometrical kind of quadric section with Ω. Each element of the collineation group Γ preserving Ω takes a subspace into one of the same type, but Γ may divide the subspaces of a given type into several transitivity classes or orbits.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

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