Words of Engel type are concise in residually finite groups. Part II
Group Theory
2019-05-21 v1
Abstract
Given a group-word w and a group G, the verbal subgroup w(G) is the one generated by all w-values in G. The word w is called concise if w(G) is finite whenever the set of w-values in G is finite. It is an open question whether every word is concise in residually finite groups. Let w=w(x_1,..,x_k) be a multilinear commutator word, n a positive integer and q a prime power. In the present article we show that the word [w^q,_n y] is concise in residually finite groups while the word [w,_n y] is boundedly concise in residually finite groups.
Keywords
Cite
@article{arxiv.1905.07784,
title = {Words of Engel type are concise in residually finite groups. Part II},
author = {Eloisa Detomi and Marta Morigi and Pavel Shumyatsky},
journal= {arXiv preprint arXiv:1905.07784},
year = {2019}
}