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Collineations of Subiaco and Cherowitzo hyperovals

1996; Volume: 3; Issue: 2 Linguagem: Inglês

10.36045/bbms/1105540790

2034-1970

Christine M. O’Keefe, J. A. Thas,

Chronic Lymphocytic Leukemia Research

A Subiaco hyperoval in PG(2; 2 h ), 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 h6 2( mod 4); a result that is already known for h 2 (mod 4). In addition, we consider a set of 2 h + 2 points in PG(2; 2 h ), where h 5i s odd, which is aC herowitzo hyperoval for h 15 and which is conjectured to form a hyperoval for all such h. We show that a collineation xing this set of points and one of the points (0; 1; 0) or (0; 0; 1) must be an automorphic collineation.