Divisible designs with dual translation group

Abstract

Many different divisible designs are already known. Some of them possess remarkable automorphism groups, so called dual translation groups. The existence of such an automorphism group enables us to characterize its associated divisible design as being isomorphic to a substructure of a finite affine space.

Divisible designs, Laguerre geometry, and beyond

“…Also, we refer to [120] for a discussion of transitive extensions of imprimitive groups. A generalisation of Spera's construction was exhibited in [54] and [56]. It was put into a more general context in [38] as follows: Let a group G acting on some set X and a starter t-DD in X be given.…”