Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-24T02:08:36.333Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Chevalley, C. C.The Algebraic theory of spinors (New York, 1954).CrossRefGoogle Scholar
(2)Dickson, L. E.Linear groups with an exposition of the Galois field theory (Leipzig, 1901).Google Scholar
(3)Dieudonné, J.Sur les groupes classigues (Paris, 1948).Google Scholar