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arXiv · 1010.4220

Relative hyperbolicity and similar properties of one-generator one-relator relative presentations with powered unimodular relator

Anton A. Klyachko·Denis E. Lurye
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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.

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Anton A. Klyachko, Denis E. Lurye. 2010-10-20. Relative hyperbolicity and similar properties of one-generator one-relator relative presentations with powered unimodular relator. https://doi.org/10.1016/j.jpaa.2011.06.020

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