Growth function of a finitely generated group
= Growth function of a finitely generated group
{title2=$\beta_{G,S}$}
For a <finitely generated group> $G$ with finite generating set $S$, the growth function $\beta_{G,S}(r)$ is the number of group elements of <word metric> distance at most $r$ from the identity. Different finite generating sets change its scale only by multiplicative constants.