English

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}
}
R2 v1 2026-06-22T03:13:02.261Z