Abstract
This chapter gives the complete description of all translation planes of order q2, having GF(q) contained in their kernels, and admitting SL(2,q) as a collineation group. Before we can give this description, we have to prove some results on ovals in finite desarguesian planes of odd order, among them Segre’s famous result that any oval in such a plane is a conic. Moreover, we have to investigate twisted cubics in projective 3-space and similar configurations in projective 3-spaces of characteristic 2.
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© 1980 Springer-Verlag New York Inc.
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Lüneburg, H. (1980). Translation Planes of Order q2 Admitting SL(2,q) as a Collineation Group. In: Translation Planes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-67412-9_7
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DOI: https://doi.org/10.1007/978-3-642-67412-9_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-67414-3
Online ISBN: 978-3-642-67412-9
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