PSG-group

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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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VIEW 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 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.

Facts