Collineations of Subiaco and Cherowitzo hyperovals
نویسندگان
چکیده
A Subiaco hyperoval in PG(2, 2h), h ≥ 4, is known to be stabilised by a group of collineations induced by a subgroup of the automorphism group of the associated Subiaco generalised quadrangle. In this paper, we show that this induced group is the full collineation stabiliser in the case h 6≡ 2 (mod 4); a result that is already known for h ≡ 2 (mod 4). In addition, we consider a set of 2h + 2 points in PG(2, 2h), where h ≥ 5 is odd, which is a Cherowitzo hyperoval for h ≤ 15 and which is conjectured to form a hyperoval for all such h. We show that a collineation fixing this set of points and one of the points (0, 1, 0) or (0, 0, 1) must be an automorphic collineation.
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