A contraction of square transversal designs Original Research Article

In this paper we show that if a square transversal design image, say image, admits a class semiregular automorphism group G of order s, then we have a image by image matrix M with entries from image satisfying image, where image, if image, and image, otherwise. As an application of image, we show that any symmetric image admits no nontrivial elation. We also obtain a result that gives us a restriction on the existence of elations of putative projective planes of composite order.