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Publication Date:
May 2006
ISSN:
1615-7168
DOI:
10.1515/ADVGEOM.2006.019

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Managing Editor: Grundhöfer, Theo / Strambach, Karl

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Two-transitive ovals

Citation Information: Advances in Geometry. Volume 6, Issue 2, Pages 323–332, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: 10.1515/ADVGEOM.2006.019, May 2006

Publication History:
Received:
2004-07-19
Published Online:
2006-05-17

Abstract

An oval 𝒪 of a projective plane is called two-transitive if there is a collineation group G fixing 𝒪 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.

Key words: Suzuki group; projective plane; oval; spread; symplectic translation plane; Lüneburg plane

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