Galois geometry

[1] More narrowly, a Galois geometry may be defined as a projective space over a finite field.

[2] Objects of study include 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.

Vector spaces defined over finite fields play a significant role, especially in construction methods.

[3] Let V = V(n + 1, q) denote the vector space of (algebraic) dimension n + 1 defined over the finite field GF(q).

In his article of 1892,[5] on proving the independence of his set of axioms for projective n-space,[6] among other things, he considered the consequences of having a fourth harmonic point be equal to its conjugate.

George Conwell gave an early application of Galois geometry in 1910 when he characterized a solution of Kirkman's schoolgirl problem as a partition of sets of skew lines in PG(3,2), the three-dimensional projective geometry over the Galois field GF(2).

At the 1958 International Mathematical Congress Segre presented a survey of results in Galois geometry known up to that time.