In 1971 Rosati showed that every sharply $3$-transitive permutation group $G$ gives rise to an affine plane $\pi$ whose projective closure contains ovals. Such ovals are of hyperbolic type as they have two infinite points. We give a characterisation of the Rosati oval in the regular nearfield plane of dimension $2$ over its centre.

### Ovals in a plane coordinatised by a regular nearfield of dimension $2$ over its centre

#### Abstract

In 1971 Rosati showed that every sharply $3$-transitive permutation group $G$ gives rise to an affine plane $\pi$ whose projective closure contains ovals. Such ovals are of hyperbolic type as they have two infinite points. We give a characterisation of the Rosati oval in the regular nearfield plane of dimension $2$ over its centre.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11563/1539