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.
Groups generated by a finite Engel set
Antonio Tortora
2011
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.File in questo prodotto:
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