LEMMA 4. The number of conics in AG(2, q) (q > 2) is greater than the number of Baer-subIines of a line in PG(2, q2).Proof. Any conic in PG(2, q) is invariant under q(qZ -1) collineations of the projective linear group, which has order qS(q3 _ 1)(q2 _ 1). Therefore the number of conics is q2(qS _ 1). The number of lines not intersecting a fixed conic is q(q -1)/2. Counting in two different ways the number b of conics not intersecting a fixed line, we obtain b = qS(q_ 1)2/2. Since a Baer-subline of a line of PG(2, q2) is determined uniquely by any three of its Geometriae Dedicata 8 (1979) 125-126. 0046-5755[79/0081-0125500.30
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