An Engel condition for orderable groups
Group Theory
2014-02-24 v1
Abstract
Let m,n be positive integers, v a multilinear commutator word and w=v^m. We prove that if G is an orderable group in which all w-values are n-Engel, then the verbal subgroup v(G) is locally nilpotent. We also show that in the particular case where v=x the group G is nilpotent (rather than merely locally nilpotent).
Keywords
Cite
@article{arxiv.1402.5247,
title = {An Engel condition for orderable groups},
author = {P. Shumyatsky and A. Tortora and M. Tota},
journal= {arXiv preprint arXiv:1402.5247},
year = {2014}
}