A Magnus theorem for some one-relator groups
Group Theory
2009-04-21 v2 Geometric Topology
Abstract
We will say that a group G possesses the Magnus property if for any two elements u,v in G with the same normal closure, u is conjugate to v or v^{-1}. We prove that some one-relator groups, including the fundamental groups of closed nonorientable surfaces of genus g>3 possess this property. The analogous result for orientable surfaces of any finite genus was obtained by the first author [Geometric methods in group theory, Contemp. Math, 372 (2005) 59-69].
Cite
@article{arxiv.0904.1143,
title = {A Magnus theorem for some one-relator groups},
author = {Oleg Bogopolski and Konstantin Sviridov},
journal= {arXiv preprint arXiv:0904.1143},
year = {2009}
}
Comments
This is the version published by Geometry & Topology Monographs on 29 April 2008. V2: typographical corrections