I started reading with growth of groups. The problem is the following:
Problem : Let $G$ be an infinite finitely generated group. a. If $G$ is polynomial growth then so is $G^m$ (a direct product of $G$). Moreover, the growth function $\gamma_G$ is not equivalent of $\gamma_{G^m}$ unless $m=1$. b. If $G$ is exponential growth then so is $G^m$, and their growth functions are equivalent.
Could any one give me a hint. Thanks in advance.
