On a characterization of the group Aut(HS)

This paper is a continuation of [12]: we begin to carry out the programme outlined in [12], adapting a more detailed approach. In this paper a geometry discovered by S. Yoshiara [19] and admitting Aut(HS) as automorphism group is considered. The interest of this geometry also lies in certain ‘irregular’ features, which give it an exceptional position among other c.C2 geometries. The uniqueness of such a geometry has been proved by R. Weiss and S. Yoshiara [18] using Cayley. Here we give another proof of that result, stressing the theory of coverings of [14, 15]. The paper is organized as follows. In Section 1 a short survey of c.C2 geometries is given. The geometry we study in this paper is described in Section 2. In Section 3 we give a general outline of the method we use (we could have referred to [12] for that, but we preferred to make this paper as self-contained as possible). The uniqueness proof is given in Sections 4 and 5. © 1991, Academic Press Limited. All rights reserved.