Groups generated by a finite Engel set

2011/09/26 by Alireza Abdollahi, Abdollahi, Alireza, Rolf Brandl +3
Mathematics · #20F19 #20F45 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20F19 #msc:20F45

paper · pdf · doi:10.48550/arxiv.1109.5439

to appear in Journal of Algebra

arxiv created 2011/09/26 · arxiv updated 2011/09/27

Abstract

A subset S of a group G is called an Engel set if, for all x,y∈ 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.

Related

• On finitely generated Engel branch groups
• On finite groups with automorphisms whose fixed points are Engel
• Finite groups with Engel sinks of bounded rank
• Engel groups with an identity
• Profinite groups with an automorphism whose fixed points are right Engel