Finite Laguerre Near-planes of Odd Order Admitting Desarguesian Derivations

AbstractWe introduce finite Laguerre near-planes and investigate such planes of odd order that admit a Desarguesian derivation

Laguerre near-planes of order four

We investigate Laguerre near-planes of order 4 and classify all such planes. We further develop various descriptions of these planes and characterise those Laguerre near-planes that can be extended to the Miquelian Laguerre plane. We also determine the automorphism groups of these planes and give characterisations of some of the planes in terms of their automorphism groups