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Galois geometry (so named after the 19th century French Mathematician √Čvariste Galois) is the branch of finite geometry that is concerned with algebraic and analytic geometry over a finite field (or Galois field).[1] More narrowly, a Galois geometry may be defined as a projective space over a finite field.[2]

Objects of study include vector spaces, affine and projective spaces over finite fields and various structures that are contained in them. In particular, arcs, ovals, hyperovals, unitals, blocking sets, ovoids, caps, spreads and all finite analogues of structures found in non-finite geometries.


Notes

SpringerLink

"Projective spaces over a finite field, otherwise known as Galois geometries, ...", (Hirschfeld & Thas 1992)

References

Hirschfeld, J. W. P. (1979), Projective Geometries Over Finite Fields, Oxford University Press, ISBN 978-0-19-850295-1, emphasizing dimensions one and two.
Hirschfeld, J. W. P. (1985), Finite Projective Spaces of Three Dimensions, Oxford University Press, ISBN 0-19-853536-8, dimension 3.
Hirschfeld, J. W. P.; Thas, J. A. (1992), General Galois Geometries, Oxford University Press, ISBN 978-0-19-853537-9, treating general dimension.

External links

Galois geometry at Encyclopaedia of Mathematics, SpringerLink

Undergraduate Texts in Mathematics

Graduate Texts in Mathematics

Graduate Studies in Mathematics

Mathematics Encyclopedia

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