"Ignatowsky showed that the only admissible transforma- tions consistent with the principle of inertia, the isotropy of space, the absence of preferred inertial frames, and a group structure (i.e., closure under composition), are the Lorentz transformations, in which c can be any veloc- ity scale, or the Galilei transformations"

The interpretation of their result is totally wrong although the result is correct, because excluding Newtons' relativity (the Galilean group) is why electromagnetism or c is necessary.