Right 4-engel elements of a group

Abstract

We prove that the set of right 4-Engel elements of a group G is a subgroup for locally nilpotent groups G without elements of orders 2, 3 or 5; and in this case the normal closure xG is nilpotent of class at most 7 for each right 4-Engel elements x of G. © 2010 World Scientific Publishing Company.