The ring Z / 3Z, or GF(3), has the elements 1, 0, and −1; its projective line has the four elements , , , since both 1 and −1 are units. The homography group on this projective line has 12 elements, also described with matrices or as permutations. For a finite field GF(q), the projective line is the Galois geometry . J. W. P. Hirschfeld has described the harmonic tetrads in the projective lines for q = 4, 5, 7, 8, 9.
