Finite geometry MOC

Galois geometry

The Galois geometry PG⁡(𝑛,𝑞) is an 𝑛-dimensional finite projective space given by the projectivization of a (𝑛 +1)-dimensional vector space over the Galois field of order 𝑞, geo i.e.

PG⁡(𝑛,𝑞)=P⁡(GF⁡(𝑞)𝑛+1)

All finite projective spaces of dimension 𝑛 ≥3 are isomorphic to a Galois geometry.¹

Properties

• Number of subspaces of a Galois geometry

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Footnotes

1. 2020. Finite geometries, ¶4.6, p. 77 ↩