The groups of projectivities of B-ovals

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It is known that the group of projectivities G of a B-oval B=(M, F) is triply-transitive on the set M. Using the classification of all finite triply-transitive groups we list the possible groups of projectivities of the finite B-ovals. Furthermore, we give a definition of hyperbolic parts that covers hyperbolic parts derived from finite B-ovals of odd order. We also list the possible groups of projectivities of finite hyperbolic parts. Following this we define algebraic B-ovals and Lie B-ovals and show that both classes contain only B-conics. Finally, we investigate real B-ovals.

Original languageEnglish
Pages (from-to)337-359
Number of pages23
JournalGeometriae Dedicata
Issue number3
Publication statusPublished - Mar 1992
Externally publishedYes

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