4-Engel implies locally nilpotent for groups

From Groupprops
Jump to: navigation, search
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., 4-Engel group) must also satisfy the second group property (i.e., locally nilpotent group)
View all group property implications | View all group property non-implications
Get more facts about 4-Engel group|Get more facts about locally nilpotent group

Statement

The statement has the following equivalent formulations:

  1. Any 4-Engel group is a locally nilpotent group.
  2. Any finitely generated 4-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

Similar facts for groups

Similar facts for Lie rings