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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A group is termed a 3-Engel group or group of Levi class two if it satisfies the following equivalent conditions:
- For all , we have that is the identity element of where denotes the group commutator. In other words, the group is a bounded Engel group of Engel degree at most three.
- Every subgroup arising as the normal subgroup generated by a singleton subset is a group of nilpotency class two.
Equivalence of definitions
Further information: equivalence of definitions of 3-Engel group
Relation with other properties
|Property||Meaning||Proof of implication||Proof of strictness (reverse implication failure)||Intermediate notions|
|group of nilpotency class two|
|group of nilpotency class three|