On the structure of the automorphism group of 2-dimensional Laguerre planes

In this note we consider 2-dimensional Laguerre planes and prove structure theorems on their automorphism group . In particular, we look at connected locally simple Lie subgroups of and the factor group / of a connected closed subgroup of over the kernel of the action of on the set of parallel classes. The informations obtained will be useful in the later classification of 2-dimensional Laguerre planes having a 4-dimensional automorphism group.Dedicated to Professor H. Salzmann on the occasion of his 60th birthday