Verbally closed virtually free subgroups
Group Theory
2023-02-14 v5
Abstract
A theorem of Myasnikov and Roman'kov says that any verbally closed subgroup of a finitely generated free group is a retract. We prove that all free (and many virtually free) verbally closed subgroups are retracts in any finitely generated group.
Keywords
Cite
@article{arxiv.1702.07761,
title = {Verbally closed virtually free subgroups},
author = {Anton A. Klyachko and Andrey M. Mazhuga},
journal= {arXiv preprint arXiv:1702.07761},
year = {2023}
}
Comments
5 pages. A Russian version of this paper is at http://halgebra.math.msu.su/staff/klyachko/papers.htm . V.5: An error in an example is corrected (Section 2); thanks to Mikhail Mikheenko