On polar ovals in abelian projective planes (Q378445)

An abelian projective plane is a projective plane which admits an abelian Singer group. Such planes have been studied by \textit{U. Ott} [Math. Z. 144, 195--215 (1975; Zbl 0305.50009)] and \textit{C. Y. Ho} [J. Algebra 208, No. 2, 533--550 (1998; Zbl 0918.51012)]. The paper in fact is based on these results. Abelian projectivc planes give rise to abelian difference sets \(D\). The authors give a condition on \(D\) such that \(2D\) is the set of absolute points of a polarity and show that such projective planes then have to be Desarguesian.