P-group of nilpotency class less than p

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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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Definition

A p-group of nilpotence class less than p is a group $G$ such that the order of every element of $G$ is the power of a particular prime number $p$, and $G$ is a nilpotent group of nilpotence class at most $p-1$.

Relation with other properties

Stronger properties

• Abelian p-group
• Odd-order class two p-group

Weaker properties

• Regular p-group
• Lazard Lie group