Abstract
We investigate, from a group-theoretical point of view, the possibility of implementing the so-called extended principle of relativity. This consists in postulating that the set of all equivalent reference frames contains frames whose relative velocities are larger than c, in addition to those whose coordinates are related by proper orthochronous Lorentz transformations. We show that implementing the extended principle of relativity by means of either real or complex linear transformations results in strong conflicts with experiment and/or intractable problems of interpretation. We then briefly analyze alternative approaches to four-dimensional superluminal transformations, in which the extended principle of relativity is either weakened or completely abandoned.