Left 3-Engel elements in groups

Abstract

In this paper we study left 3-Engel elements in groups. In particular, we prove that for any prime p and any left 3-Engel element x of finite p-power order in a group G, xp is in the Baer radical of G. Also it is proved that 〈x,y〉 is nilpotent of class at most 4 for every two left 3-Engel elements in a group G. © 2003 Elsevier B.V. All rights reserved.