Right 4-Engel elements of a group

A. Abdollahi; H. Khosravi

Right 4-Engel elements of a group

Group Theory 2010-01-26 v1

Authors: A. Abdollahi , H. Khosravi

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 $<x>^G$ is nilpotent of class at most 7 for each right 4-Engel elements $x$ of $G$ .

Keywords

nilpotent groups finite group theory

Cite

@article{arxiv.1001.4156,
  title  = {Right 4-Engel elements of a group},
  author = {A. Abdollahi and H. Khosravi},
  journal= {arXiv preprint arXiv:1001.4156},
  year   = {2010}
}

Comments

to appear in Journal of Algebra and its Applications; This paper has some overlaps with arXiv:0906.2439, however the proofs are clearer and arXiv:0906.2439 will not publish anywhere

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