On elation Laguerre planes with a two-transitive orbit on the set of generators
Finite elation Laguerre planes were introduced in [the first author, J. Geom. 41, No 1--2, 162--179 (1991; Zbl. 0737.51003)]. They are characterized by the existence of a group of automorphisms acting trivially on the set of generators and sharply transitively on the set of circles. The main result of the paper is a characterization of miquelian Laguerre planes over \(\mathrm{GF}(q)\) in the case \(q\) odd. It is proved that the finite elation Laguerre planes of odd order \(q\) are precisely the miquelian Laguerre planes over \(\mathrm{GF}(q)\) when they have an automorphism group fixing a generator and acting 2-transitively on the set of remaining generators. For \(q\) even non-miquelian examples exist, but for \(q=2^e\) with \(e\) a prime or a square of a prime, the Laguerre plane is always ovoidal over a translation oval.
scientific article; zbMATH DE number 6914843
scientific article