Engel groups with an identity
Group Theory
2018-06-01 v1
Abstract
We give an affrmative answer to the question whether a residually finite Engel group satisfying an identity is locally nilpotent. More generally, for a residually finite group G with an identity, we prove that the set of right Engel elements of G is contained in the Hirsch-Plotkin radical of G. Given an arbitrary word w, we also show that the class of all groups G in which the w-values are right n-Engel and w(G) is locally nilpotent is a variety.
Keywords
Cite
@article{arxiv.1805.12411,
title = {Engel groups with an identity},
author = {Pavel Shumyatsky and Antonio Tortora and Maria Tota},
journal= {arXiv preprint arXiv:1805.12411},
year = {2018}
}