Lazard Lie group

The article defines a property of groups, where the definition may be in terms of a particular prime that serves as parameter
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Definition

A group of prime power order is termed a Lazard Lie group if every subgroup of it generated by three elements, has nilpotence class at most $p-1$ where $p$ is the prime associated with the group.

Facts

Lazard's theorem gives a method to construct a Lie algebra for any Lazard Lie group. This construction and its paraphernalia go under the name of the Lazard correspondence.