# P-group of nilpotency class less than p

From Groupprops

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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

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

A **p-group of nilpotence class less than p** is a group such that the order of every element of is the power of a particular prime number , *and* is a nilpotent group of nilpotence class at most .