Algebraic structure of coordinates of a translation transversal design (Q1119650)

Let D be a transversal design which admits a group G acting regularly on the point set such that one has \(B=B^ g\) or \(B\cap B^ g=\emptyset\) for every block B and every group element g. Such a TD is called a translation transversal design (TTD). TTD's have been extensively studied starting with the fundamental paper by \textit{R. H. Schulz} [``Transversal designs and partitions associated with Frobenius groups'', J. Reine Angew. Math. 355, 153-162 (1985; Zbl 0546.05015)]. The present authors give an algebraic description of TDD's in terms of ``transversal modules''.