# PSG-group

From Groupprops

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism

View a complete list of group propertiesVIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

*This property makes sense for infinite groups. For finite groups, it is always true*

## Definition

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