Dale said:
I guess the right way to say it is "nothing can travel faster than c, but light can travel slower than c in a transparent medium."
Edit: I see jbriggs444 said almost exactly the same thing.
Well, that's a bit more complicated, because you have to specify which "speed" you are referring to when talking about "travel speed" of waves in a dispersive medium.
First you look at stationary states of single-frequency plane waves traveling in ##x## direction, which are of the form
$$A(t,\vec{x})=A_0 \exp(-\mathrm{i} \omega t + \mathrm{i} n(\omega) \omega x).$$
Here ##A## is some arbitrary field (e.g., a component of the electromagnetic field). If it's a real quantity, we silently take the real part of the exponential form, which is just more convenient to calculate with. Then ##n(\omega)## is a frequency dependent diffraction index, which in general is complex, describing both dispersion (real part) and damping (imaginary part) of the waves in the medium. If we have weak damping, i.e., if we can neglect the imaginary part of ##n(\omega)## we can define the
phase velocity, defined by setting the phase of the wave constant
$$\omega t-\omega n(\omega) x=\text{const} \; \Rightarrow \; c_{\text{phase}}= \mathrm{d}x/\mathrm{d} t=1/n(\omega).$$
There's nothing preventing ##n(\omega)<1##, and thus ##c_{\text{phase}}## can be ##>1## (I'm setting the speed of light in vacuo to 1 of course). This doesn't violate Einstein causality, because it's a "speed" of a stationary plane-wave state, which in nature can only be reached approximately in a limited region of space by switching on such a harmonic signal for a sufficiently long time. The speed doesn't refer to any cause-and-effect relationship between "events". It's just defining the speed of the propagation of the phase of a stationary plane wave.
Another question is, how fast signals can travel, i.e., the speed of a wave packet of limited spatial width. Such a wave packet is constructed by a Fourier transform, i.e., the decomposition of the wave in the plane-wave modes
$$A(t,x)=\int_{\mathbb{R}} \mathrm{d} \omega \frac{1}{2 \pi} A_{\omega_0}(\omega) \exp [-\mathrm{i} \omega t + \mathrm{i} k(\omega) x], \quad k(\omega)=\omega n(\omega).$$
Suppose now that ##A_{\omega_0}## is quite narrowly peaked around a single frequency. Then we can approximate the integral as
$$A(t,x) \simeq \exp[-\mathrm{i} \omega_0 t+\mathrm{i} k(\omega_0) x] \int_{\mathbb{R}} \mathrm{d} \omega' \frac{A_{\omega_0}(\omega_0+\omega)}{2 \pi} \exp \left [\mathrm{i} \frac{\omega'}{v_g} (x-v_g t) \right]$$
with
$$v_g=\left (\frac{\mathrm{d} k}{\mathrm{d} \omega} \right)^{-1}_{\omega=\omega_0}.$$
Thus the "envelope" of the wave packet (characterized, e.g., by its peak) goes with the group velocity ##v_g##. Also this quantity can take values ##>c## (in the region of anomalous dispersion).
The only speed that can never exceed the speed of light is the front velocity of a wave of finite spatial extension. This has been shown already around 1910 by Sommerfeld in answer to a question by W. Wien, how the faster-than-light phase and group velocities well known in optics are compatible with the special theory of relativity.
