  We investigate the connection between the abelian rank of a countable
amenable group and the existence of good averaging sequences (e.g. for the
pointwise ergodic theorem). We show that if $G$ is a group of abelian rank
$r(G)$ then any Tempel'man sequence must have constant at least $2^{r(G)}$ and
if $G$ is abelian this constant is achieved. On the other hand, infinite rank
excludes the existence of Tempel'man sequences and forces all tempered
sequences to grow super-exponentially.
