PSG-group

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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This property makes sense for infinite groups. For finite groups, it is always true

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 $n$.