Transversal designs associated with frobenius groups

To any Frobenius group G (of degree s, with Frobenius complement of order k) we associate an (s,k) -transversal design (G) which admits G as a point-regular collineation group. (G) is in fact also a dual translation net and furthermore admits a flag-regular collineation group. Also, (G) has two orthogonal resolutions. Conversely, we will characterize the Frobenius groups among the point-regular collineation groups of resolvable transversal designs. We also exhibit two further classes of flag-regular transversal designs. Finally, we completely determine the possible parameters of TD's constructed as above.Dedicated to Professor R. Artzy on the occasion of his 70th birthday