Groups generated by a finite Engel set

Alireza Abdollahi; Rolf Brandl; Antonio Tortora

Groups generated by a finite Engel set

Group Theory 2011-09-27 v1

Authors: Alireza Abdollahi , Rolf Brandl , Antonio Tortora

Abstract

A subset $S$ of a group $G$ is called an Engel set if, for all $x,y\in S$ , there is a non-negative integer $n=n(x,y)$ such that $[x,\,_n y]=1$ . In this paper we are interested in finding conditions for a group generated by a finite Engel set to be nilpotent. In particular, we focus our investigation on groups generated by an Engel set of size two.

Keywords

nilpotent groups finite group theory

Cite

@article{arxiv.1109.5439,
  title  = {Groups generated by a finite Engel set},
  author = {Alireza Abdollahi and Rolf Brandl and Antonio Tortora},
  journal= {arXiv preprint arXiv:1109.5439},
  year   = {2011}
}

Comments

to appear in Journal of Algebra

Groups generated by a finite Engel set

Abstract

Keywords

Cite

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