On left Hadamard transversals in non-solvable groups Original Research Article

Let image be a group of order image and image an involution of image. A image-subset image of image is called a left Hadamard transversal of image with respect to image if image and image for some subsets image and image of image. Let image be a subgroup of image such that image, image, and image, where image is the conjugacy class of image and image is the commutator subgroup of image. In this article, we show that if image satisfies a condition image, then image is a image relative difference set and one can construct a image integral matrix image such that image, where image is a positive integer determined by image and image (see Theorem 2.6). Using this we show that there is no left Hadamard transversal image satisfying image in some simple groups.