2. Notation and preliminary results. Let K = F (0) be a cyclic Galois extension of degree 3 of the field F and denote by K ~ x--* ff s K an automorphism which generates Ga l (K :F ) . Represent the points of PG(2, K) by P = ( ( x l , x 2 , x3) ) and lines by 9 = ((Yl, Y2, Y3) t) (xl, Yl ~ K) and P lies on 9 if and only if 52 xiyi = 0. The action of i G = PGL(3, F) is given by P7 = (vT}, g7 = (7 lug} for 7 ~ G, P = (v}, and g = (u t} (we identify the elements of G with their pre-images in GL (3, F)). Denote by N the set of points and by 5r the set of lines of PG(2, K). Define partitions N = ~1 w ~2 k..) ~ 3 and 5r = ~1 w ~W 2 w ~~ 3 where ( (x l , x2, x3)} e Ni (respectively ((xl , x2, x3) t} e ~i) if and only if d imF(x 1,x 2 , x 3 } = i . Now S = ( ( 1 , 0 , 0 2 ) } , S l = ( ( 1 , O , f f 2 ) } , and $2 = ((1, 0, g2)} are points of ~3 and s = $1 9 $2 e 5~ Pick the t ransformation matrix Te GL(3, K) such that N1 is maped onto the set {((x, if, 2 ) ) Ix e K} (see [1] and [2]). Images under this t ransformation are denoted by .Then G is induced by regular matrices of the form