Moufang lines defined by (generalized) Suzuki groups

We show that the automorphism group of a geometry defined by the generalized Suzuki groups is contained in the automorphism group of the corresponding Suzuki group. This shows that the study of these groups is equivalent to the study of those geometries. This completes, for the Suzuki groups as split BN-pairs of rank 1, a program set up by Jacques Tits some years ago. We also provide a similar result for the generalized Suzuki–Tits inversive planes related to these groups.