# Fixed-class capable group

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

## Definition

Suppose is a positive number. A group is a **class -capable group** if there exists a group such that where denotes the member of the upper central series of .

Note that is the center and class 1-capable group is the same notion as capable group.