Free subgroups of one-relator relative presentations
Group Theory
2007-09-02 v3
Abstract
Suppose that G is a nontrivial torsion-free group and w is a word over the alphabet G\cup\{x_1^{\pm1},...,x_n^{\pm1}\}. It is proved that for n\ge2 the group \~G=<G,x_1,x_2,...,x_n | w=1> always contains a nonabelian free subgroup. For n=1 the question about the existence of nonabelian free subgroups in \~G is answered completely in the unimodular case (i.e., when the exponent sum of x_1 in w is one). Some generalisations of these results are discussed.
Cite
@article{arxiv.math/0510582,
title = {Free subgroups of one-relator relative presentations},
author = {Anton A. Klyachko},
journal= {arXiv preprint arXiv:math/0510582},
year = {2007}
}
Comments
V3: A small correction in the last phrase of the proof of Theorem 1. 4 pages