Automorphism groups of tetravalent Cayley graphs on regular image-groups

Let image be a connected tetravalent Cayley graph on a regular p-group G and let image be the automorphism group of G. In this paper, it is proved that, for each prime image, the automorphism group of the Cayley graph image is the semidirect product image where image is the right regular representation of G and image. The proof depends on the classification of finite simple groups. This implies that if image then the Cayley graph image is normal, namely, the automorphism group of image contains image as a normal subgroup.