Groups generated by a finite Engel set

Details Groups generated by a finite Engel set Groups generated by a finite Engel set

2011-09-26

arxiv.org/abs/1109.5439v1

Mathematics

Group Theory

to appear in Journal of Algebra

Scientific paper

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.

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