PSG-group

Definition
For an infinite group $$G$$, let $$s_n(G)$$ denote the number of subgroups of index at most $$n$$ in $$G$$. Then, $$G$$ is said to be a PSG-group, or is said to have Polynomial Subgroup Growth if $$s_n(G)$$ is bounded from above by a polynomial function of $$n$$.