ABSTRACT
In this chapter, constructions of Kantor [156] are given of transitive t-spreads that admit a retraction group that construct interesting subgeometry partitions. Actually, these t-spreads also produce ‡agtransitive designs. Although there are variations on the types given, there are four main classes of ‡ag-transitive designs. In this chapter, we shall discuss the two ‡ag-transitive designs that admit cyclic transitive linear subgroups. In the next chapters, the partitions that admit cyclic transitive t-spreads are then used to construct new subgeometry partitions. The reader is directed to Kantor [156] for a description of the other two main classes. These classes admit a transitive linear group on the associated t-spread that contains a cyclic subgroup of index 2.
