Relative hyperbolicity and similar properties of one-generator one-relator relative presentations with powered unimodular relator
Group Theory
2015-03-17 v3
Abstract
A group obtained from a nontrivial group by adding one generator and one relator which is a proper power of a word in which the exponent-sum of the additional generator is one contains the free square of the initial group and almost always (with one obvious exception) contains a non-abelian free subgroup. If the initial group is involution-free or the relator is at least third power, then the obtained group is SQ-universal and relatively hyperbolic with respect to the initial group.
Keywords
Cite
@article{arxiv.1010.4220,
title = {Relative hyperbolicity and similar properties of one-generator one-relator relative presentations with powered unimodular relator},
author = {Anton A. Klyachko and Denis E. Lurye},
journal= {arXiv preprint arXiv:1010.4220},
year = {2015}
}
Comments
11 pages. A Russian version of this paper is at http://mech.math.msu.su/department/algebra/staff/klyachko/papers.htm V3: revised following referee's comments