An oval script O sign of a projective plane is called two-transitive if there is a collineation group G fixing script O sign and acting 2-transitively on its points. If the plane has odd order, then the plane is desarguesian and the oval is a conic. In the present paper we prove that if a plane has order a power of two and admits a two-transitive oval, then either the plane is desarguesian and the oval is a conic, or the plane is dual to a Lüneburg plane. © de Gruyter 2006.
Two-transitive ovals / Maschietti, Antonio. - In: ADVANCES IN GEOMETRY. - ISSN 1615-715X. - STAMPA. - 6:2(2006), pp. 323-332. [10.1515/advgeom.2006.019]
Two-transitive ovals
MASCHIETTI, Antonio
2006
Abstract
An oval script O sign of a projective plane is called two-transitive if there is a collineation group G fixing script O sign and acting 2-transitively on its points. If the plane has odd order, then the plane is desarguesian and the oval is a conic. In the present paper we prove that if a plane has order a power of two and admits a two-transitive oval, then either the plane is desarguesian and the oval is a conic, or the plane is dual to a Lüneburg plane. © de Gruyter 2006.File allegati a questo prodotto
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