  We study the frog model on Cayley graphs of groups with polynomial growth
rate $D \geq 3$. The frog model is an interacting particle system in discrete
time. We consider that the process begins with a particle at each vertex of the
graph and only one of these particles is active when the process begins. Each
activated particle performs a simple random walk in discrete time activating
the inactive particles in the visited vertices. We prove that the activation
time of particles grows at least linearly and we show that in the abelian case
with any finite generator set the set of activated sites has a limiting shape.
