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

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 1 , July 1970 , pp. 33 - 43
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

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