On the right and left 4-engel elements

Abstract

In this article we study left and right 4-Engel elements of a group. In particular, we prove that (a ab) is nilpotent of class at most 4, whenever a is of finite order and b±1 are right 4-Engel elements or a±1 are left 4-Engel elements and b is an arbitrary element of G. Furthermore, we prove that for any prime p and any element a of finite p-power order in a group G such that a±1 ∈ L4(G), a4, if p = 2, and ap, if p is an odd prime number, is in the Baer radical of G. © Taylor & Francis Group, LLC.