Vol. 6+7, No. 1, 2008

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Groups of hyperovals in Desarguesian planes

Luke Bayens, William Cherowitzo and Tim Penttila

Vol. 6+7 (2008), No. 1, 37–51

We show that if a hyperoval of PG2q, q > 4, admits an insoluble group G, then G fixes a subplane π0 of order q0 > 2, meets π0 in a regular hyperoval of π0 on which G PGL3q induces PGL2q0, and if is not regular then q > q02. We also bound above the order of the homography stabilizer of a non-translation hyperoval of PG2q by 3(q 1). Finally, we show that the homography stabilizer of the Cherowitzo hyperovals is trivial for q > 8.

hyperoval, group
Mathematical Subject Classification 2000
Primary: 51E20, 51E21
Received: 1 March 2008
Accepted: 17 March 2008
Luke Bayens
William Cherowitzo
University of Colorado at Denver
United States
Tim Penttila