On groups admitting a word whose values are Engel
Group Theory
2015-07-17 v1
Abstract
Let m, n be positive integers, v a multilinear commutator word and w = v^m. We prove that if G is a residually finite group in which all w-values are n-Engel, then the verbal subgroup w(G) is locally nilpotent. We also examine the question whether this is true in the case where G is locally graded rather than residually finite. We answer the question affirmatively in the case where m = 1. Moreover, we show that if u is a non-commutator word and G is a locally graded group in which all u-values are n-Engel, then the verbal subgroup u(G) is locally nilpotent.
Keywords
Cite
@article{arxiv.1208.5623,
title = {On groups admitting a word whose values are Engel},
author = {Raimundo Bastos and Pavel Shumyatsky and Antonio Tortora and Maria Tota},
journal= {arXiv preprint arXiv:1208.5623},
year = {2015}
}