3-Engel implies locally nilpotent for groups
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., 3-Engel group) must also satisfy the second group property (i.e., locally nilpotent group)
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The statement has the following equivalent formulations:
- Any 3-Engel group is a locally nilpotent group.
- Any finitely generated 3-Engel group is a nilpotent group. (In fact, we can work out an explicit bound on the nilpotency class of the group in terms of the size of the generating set).