Does a group velocity larger than c violate relativity?

It is often assumed that relativity restricts the group velocity to be less than the speed of light. In this article, this assumption is examined in the context of electromagnetic waves propagating through a dilute plasma. The index of refraction is found from the phase shift in a thin slab of plasma. The response of the same slab to a incident δ-function pulse is also found. After passing through the slab, the pulse acquires a constant tail, in the limit of a thin slab, and the response to an oscillatory wave is recovered by superposition. By considering a material in which the tail has the opposite sign, it is shown that the group velocity can be larger than c without having any signal propagate faster than c.