3-Engel implies locally nilpotent for groups

Statement
The statement has the following equivalent formulations:


 * 1) Any 3-Engel group is a locally nilpotent group.
 * 2) 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).

Related facts

 * 3-Engel implies locally nilpotent for Lie rings
 * 2-Engel implies class three for groups, 2-Engel implies class three for Lie rings
 * 4-Engel implies locally nilpotent for groups