2-Engel implies class three for groups

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

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

Similar facts for other Engel conditions

 * 3-Engel implies locally nilpotent for groups
 * 4-Engel implies locally nilpotent for groups
 * 3-Engel and (2,5)-torsion-free implies class four for groups
 * 4-Engel and (2,3,5)-torsion-free implies class seven for groups