ON FLAG-TRANSITIVE AFFINE PLANES OF ORDER-Q(3)

Let pi be a translation plane of order q3, q an odd prime power, whose kern superset-or-equal-to GF(q). Let l(infinity) be the line at infinity of pi. Let G be a solvable collineation group of pi in the linear translation complement, which acts transitively on l(infinity), and let H be maximal normal a cyclic subgroup of G. Then the restriction H of H on l(infinity) acts semiregularly on l(infinity) and \G:H\ is-an-element-of {1, 2, 3, 6}, where G is the restriction of G on l(infinity) (if q is not identically equal to -1 (mod 3), then \G:H\ is-an-element-of {1, 2}). If q is-an-element-of {3, 5} and \G:H\ is-an-element-of {1, 2}, then pi is determined completely, using a computer.