Relative growth of subgroups in finitely generated groups
Appears in collection : 2014 - T1 - Random walks and asymptopic geometry of groups.
Let $H$ be a subgroup of a finitely generated group $G$. The (relative) growth function $f(n)$ of $H$ with respect to a finite set $A$ generating $G$, is given by the formula $f(n) = card {g\in H; |g|_A \le n}$. I want to review some recent results on the asymptotic behavior of relative growth functions in free, solvable and other groups.
