Left 3-Engel elements in groups

Alireza Abdollahi

Left 3-Engel elements in groups

Group Theory 2007-05-23 v2

Authors: Alireza Abdollahi

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 $G$ , $x^p$ is in the Baer radical of $G$ . Also it is proved that $<x,y>$ is nilpotent of class 4 for every two left 3-Engel elements in a group $G$ .

Keywords

finite groups

Cite

@article{arxiv.math/0212332,
  title  = {Left 3-Engel elements in groups},
  author = {Alireza Abdollahi},
  journal= {arXiv preprint arXiv:math/0212332},
  year   = {2007}
}

Comments

A serious error in the proof Theorem 1.2, the correct proof, also correcting some misprints

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