# 2-Engel implies class three for groups

From Groupprops

This article gives the statement and possibly, proof, of an implication relation between two group properties. That is, it states that every group satisfying the first group property (i.e., 2-Engel group) must also satisfy the second group property (i.e., group of nilpotency class three)

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## Contents

## Statement

Any 2-Engel group must be a group of nilpotency class three.

## Related facts

### Similar facts for 2-Engel

- 2-Engel implies class three for Lie rings
- 2-Engel and 3-torsion-free implies class two for groups
- 2-Engel and 3-torsion-free implies class two for Lie rings