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Abstract
This paper presents the fully relativistic, general expression for the group velocity Vg of the electromagnetic wave packet in a relativistic dispersive medium. Motion of the medium is accounted for with the relativistic index of refraction. The general formula for Vg is specialized to a few particular situations that are briefly discussed. The explicit, exact, fully relativistic expression for Vg is relevant to all issues where the electromagnetic wave packet travels through a medium in motion, especially where the velocity of the medium is high or utmost accuracy is essential, e.g. it pertains to the slow light phenomenon, pulsar radiation, GPS, radar, and LIDAR technologies.