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We also define Ux = {(0,1, z) : zq+1 = -l},C/ 2 = {(1,0, z) : zq+x = - 1 } , and U3 = {(l,y,0) : yq+1 = - 1 } . Then it is trivial to see that I U Ra I U U\ U C/2 U C/3 is a partition of the points of Ti. The key ingredient is that the RJs are "triply ruled," as we now describe. We use [-,-,-] to denote line coordinates in TT, and we normalize line coordinates from the right. One easily checks that (z,2/,z) x = [xq,yq,zq] because of our choice for H. For each a £ F, let Ha = {[u,0,l] : uq+1 = a},Va = {[^,1,0] : ti« +1 = - ( 1 + a)}, and Da = {[0,17,1] : ^ + 1 - - a / ( l + a)}.

5 Let q > 2 be a prime power with q ^ 0 (mod 3). Let Go = {(cr, M) G G : cr = id or a = aq}y where G is the pointwise stabilizer of the vertices of A as described above and aq is the automorphism of GF(q2) that maps x —> xq. Then Go ^ H. 27 BAKER ET AL. : Proof. L e t (a,M) SPREADS OF HERMITIAN CURVES G Go. Write M = /I 0 0 A 0\ 0 for s o m e X,S G N. T h e \ 0 0 SJ points of B are of three types. Suppose first that a G AH. Then B will contain q -f 1 points corresponding to this element a, namely the poles of the lines of Ha = {[u,0,l] : u* +1 = a}.

Hughes, and J. A. Thas, editors, Advances in Finite Geometries and Designs, pages 35-46, Oxford, New York, Tokyo, 1991. Oxford University Press. [2] A. Blokhuis and F. Mazzocca. Special point sets in PG(n, q) and the structure of sets with the maximal number of nuclei. J. , 41, pp. 33-41, 1991. [3] A. Blokhuis and H. A. Wilbrink. A characterization of exterior lines of certain sets of points in PG(2, q). Geom. Dedicate 23, pp. 253-254, 1987. [4] A. A. Bruen. Nuclei of sets of q + 1 points in PG(2, q) and blocking sets of Redei type.