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2013 | OriginalPaper | Chapter

9. Embedding Polar Spaces in Absolutes

Authors : Francis Buekenhout, Arjeh M. Cohen

Published in: Diagram Geometry

Publisher: Springer Berlin Heidelberg

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Abstract

In Theorems 8.3.16 and 8.4.25, we saw that the most common nondegenerate polar spaces (cf. Definition 7.4.1) of rank at least three are embeddable in a projective space. So, in the continued study of a nondegenerate polar space Z of rank at least three, it is a mild restriction to assume that Z is embedded in a projective space ℙ. Still, the methods used in this chapter only require that the rank of Z be at least two.

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previous chapter Projective Embeddings of Polar Spaces

next chapter Classical Polar Spaces

E. Artin, Geometric Algebra (Interscience, New York, 1957) MATH

53.

F. Buekenhout, C. Lefèvre, Generalized quadrangles in projective spaces. Arch. Math. (Basel) 25, 540–552 (1974) MathSciNetMATHCrossRef

54.

F. Buekenhout, C. Lefèvre, Semi-quadratic sets in projective spaces. J. Geom. 7, 17–42 (1976) MATHCrossRef

59.

P.J. Cameron, W.M. Kantor, 2-transitive and antiflag transitive collineation groups of finite projective spaces. J. Algebra 60, 384–422 (1979) MathSciNetMATHCrossRef

78.

A.M. Cohen, B.N. Cooperstein, On the local recognition of finite metasymplectic spaces. J. Algebra 125, 348–366 (1989) MathSciNetMATHCrossRef

104.

H. Cuypers, The geometry of secants in embedded polar spaces. Eur. J. Comb. 28, 1455–1472 (2007) MathSciNetMATHCrossRef

118.

K.J. Dienst, Verallgemeinerte Vierecke in projektiven Räumen. Arch. Math. (Basel) 35, 177–186 (1980) MathSciNetMATHCrossRef

132.

D. Goldstein, R.M. Guralnick, L. Small, E. Zelmanov, Inversion invariant additive subgroups of division rings. Pac. J. Math. 227, 287–294 (2006) MathSciNetMATHCrossRef

159.

I.N. Herstein, Semi-homomorphisms of groups. Can. J. Math. 20, 384–388 (1968) MathSciNetMATHCrossRef

165.

L.-K. Hua, Some properties of a sfield. Proc. Natl. Acad. Sci. USA 35, 533–537 (1949) MATHCrossRef

166.

L.K. Hua, On semi-homomorphisms of rings and their applications in projective geometry. Usp. Mat. Nauk (N.S.) 8, 143–148 (1953) MATH

179.

P.M. Johnson, Semiquadratic sets and embedded polar spaces. J. Geom. 64, 102–127 (1999) MathSciNetMATH

211.

S. Mattarei, Inverse-closed additive subgroups of fields. Isr. J. Math. 159, 343–347 (2007) MathSciNetMATHCrossRef

250.

W.R. Scott, Half-homomorphisms of groups. Proc. Am. Math. Soc. 8, 1141–1144 (1957) CrossRef

278.

J.A. Thas, H. van Maldeghem, Embedded thick finite generalized hexagons in projective space. J. Lond. Math. Soc. (2) 54, 566–580 (1996) CrossRef

286.

J. Tits, Buildings of Spherical Type and Finite BN-Pairs. Lecture Notes in Mathematics, vol. 386 (Springer, Berlin, 1974) MATH

307.

A.L. Wells Jr., Universal projective embeddings of the Grassmannian, half spinor, and dual orthogonal geometries. Q. J. Math. Oxford Ser. (2) 34, 375–386 (1983) MATHCrossRef

Title: Embedding Polar Spaces in Absolutes
Authors: Francis Buekenhout
Arjeh M. Cohen
Publisher: Springer Berlin Heidelberg
Book: Diagram Geometry
Print ISBN: 978-3-642-34452-7

Electronic ISBN: 978-3-642-34453-4

Copyright Year: 2013
DOI: https://doi.org/10.1007/978-3-642-34453-4_9

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