Let P be a projective plane of order 15 with an oval O. Assume P admits a collineation group G fixing O such that G is isomorphic to A_4 and the action of G on O yields precisely two orbits O(1) and O(2) with |O(2)|= 4. We prove that the Buekenhout oval arising from O cannot exist.
On the non-existence of a projective plane of order 15 with an A_4-invariant oval / A., Aguglia; Bonisoli, Arrigo. - In: DISCRETE MATHEMATICS. - ISSN 0012-365X. - STAMPA. - 288:(2004), pp. 1-7. [10.1016/j.disc.2004.06.018]
On the non-existence of a projective plane of order 15 with an A_4-invariant oval
BONISOLI, Arrigo
2004
Abstract
Let P be a projective plane of order 15 with an oval O. Assume P admits a collineation group G fixing O such that G is isomorphic to A_4 and the action of G on O yields precisely two orbits O(1) and O(2) with |O(2)|= 4. We prove that the Buekenhout oval arising from O cannot exist.
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